Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving...
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Transcript of Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving...
![Page 1: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/1.jpg)
Linear System of Equations• Classify Systems• Independent• Dependent• Inconsistent
Methods for Solving• Tables• Graphing• Substitution• Elimination• Matrices
-5 5
-5
5
x
y
{𝑦=𝑥+3𝑥+𝑦=1
−2 1 3
−1 2 2
0 3 1[−𝟏 𝟏𝟏 𝟏
∨𝟑𝟏 ] [𝟏 𝟎
𝟎 𝟏|−𝟏𝟐 ]
(−1 ,2)
![Page 2: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/2.jpg)
Linear System of Inequalities
{−𝒙+𝟐 𝒚 ≤𝟒𝒙+𝒚<𝟖𝒙 ≥𝟐𝒚 ≥𝟏
-1 10-1
10
x
y
-1 10-1
10
x
y
-1 10-1
10
x
y
x
y
x
yMaximize:
Pg. 187 #1 – 13
![Page 3: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/3.jpg)
Linear SystemsClassifying
Systems
Solving 2 Variable Systems
Solving 3 Variable Systems
Inequalities Modeling(Application)
10 10 10 10 10
20 20 20 20 20
30 30 30 30 30
40 40 40 40 40
50 50 50 50 50
![Page 4: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/4.jpg)
Answer
Without graphing, classify each system. (independent, dependent, inconsistent)
{ 5𝑥+3 𝑦=9
𝑦=− 35𝑥+3
![Page 5: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/5.jpg)
Without graphing, classify each system. (independent, dependent, inconsistent)
{ 5𝑥+3 𝑦=9
𝑦=− 35𝑥+3
Independent
![Page 6: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/6.jpg)
Answer
Without graphing, classify each system. (independent, dependent, inconsistent)
{12𝑥−4 𝑦=20𝑦=3𝑥+3
![Page 7: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/7.jpg)
Without graphing, classify each system. (independent, dependent, inconsistent)
{12𝑥−4 𝑦=20𝑦=3𝑥+3
Inconsistent
![Page 8: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/8.jpg)
Answer
Without graphing, classify each system. (independent, dependent, inconsistent)
{2𝑥+6 𝑦=12
𝑦=− 13𝑥+2
![Page 9: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/9.jpg)
Without graphing, classify each system. (independent, dependent, inconsistent)
{2𝑥+6 𝑦=12
𝑦=− 13𝑥+2
Dependent
![Page 10: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/10.jpg)
Answer
Without graphing, classify each system. (independent, dependent, inconsistent)
{−12 𝑥+2 𝑦=−1518 𝑥−3 𝑦=27
![Page 11: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/11.jpg)
Without graphing, classify each system. (independent, dependent, inconsistent)
{−12 𝑥+2 𝑦=−1518 𝑥−3 𝑦=27
Inconsistent
![Page 12: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/12.jpg)
Answer
Without graphing, classify each system. (independent, dependent, inconsistent)
{15 𝑥+6 𝑦=610 𝑥+4 𝑦=4
![Page 13: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/13.jpg)
Without graphing, classify each system. (independent, dependent, inconsistent)
{15 𝑥+6 𝑦=610 𝑥+4 𝑦=4
Dependent
![Page 14: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/14.jpg)
-5 5
-5
5
x
y
Answer
Solve the system by: Graphing
{ 𝑦=2 𝑥−4𝑥−4 𝑦=−3
![Page 15: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/15.jpg)
Solve the system by: Graphing
{ 𝑦=2 𝑥−4𝑥−4 𝑦=−12
-5 5
-5
5
x
y
(4 , 4)
![Page 16: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/16.jpg)
Answer
Solve the system by: Substitution
{−2 𝑥− 𝑦=−9𝑦=−5 𝑥+15
![Page 17: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/17.jpg)
Solve the system by: Substitution
{−2 𝑥− 𝑦=−9𝑦=−5 𝑥+15
(2 ,5)
![Page 18: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/18.jpg)
Answer
Solve the system by: Elimination
{−8 𝑥−7 𝑦=−285 𝑥+6 𝑦=24
![Page 19: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/19.jpg)
Solve the system by: Elimination
{−8 𝑥−7 𝑦=−285 𝑥+6 𝑦=24
(0 ,4)
![Page 20: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/20.jpg)
Answer
Solve the system by: Your Choice
{6 𝑦+11+𝑥=08 𝑥=−4−6 𝑦
![Page 21: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/21.jpg)
Solve the system by: Your Choice
{6 𝑦+11+𝑥=08 𝑥=−4−6 𝑦
(1 ,−2)
![Page 22: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/22.jpg)
Answer
Solve the system by: Your Choice
{ −4 𝑦=8 𝑥+120=18 𝑦+12𝑥−90
![Page 23: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/23.jpg)
Solve the system by: Your Choice
{ −4 𝑦=8 𝑥+120=18 𝑦+12𝑥−90
(−6 ,9)
![Page 24: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/24.jpg)
Answer
Write a matrix to represent the system.
{ 6 𝑥+2 𝑦+𝑧=30−3𝑥+3 𝑧=0
−2 𝑥+5 𝑦+4 𝑧=3
![Page 25: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/25.jpg)
Write a matrix to represent the system.
{ 6 𝑥+2 𝑦+𝑧=30−3𝑥+3 𝑧=0
−2 𝑥+5 𝑦+4 𝑧=3
[ 6 2 1−3 0 3−2 5 4|
3 003 ]
![Page 26: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/26.jpg)
Answer
What system is represented by the matrix:
[2 7 13 −2 01 2 1|
960 ]
![Page 27: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/27.jpg)
What system is represented by the matrix:
{2𝑥+7 𝑦+𝑧=93 𝑥−2 𝑦=6𝑥+2 𝑦+𝑧=0
[2 7 13 −2 01 2 1|
960 ]
![Page 28: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/28.jpg)
Answer
Solve the system by: Your Choice
{ 6 𝑥−5 𝑧=−11𝑥− 𝑦=−12
−4 𝑥−4 𝑦+5 𝑧=−25
![Page 29: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/29.jpg)
Solve the system by: Your Choice
{ 6 𝑥−5 𝑧=−11𝑥− 𝑦=−12
−4 𝑥−4 𝑦+5 𝑧=−25
[ 6 0 −51 −1 0−4 −4 5 |−11
−12−25 ] (−6 ,6 ,−5)
![Page 30: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/30.jpg)
Answer
Solve the system by: Your Choice
{6 𝑥−5 𝑦+𝑧=−172 𝑥− 𝑦+𝑧=−5𝑧=−3𝑥−8
![Page 31: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/31.jpg)
Solve the system by: Your Choice
{6 𝑥−5 𝑦+𝑧=−172 𝑥− 𝑦+𝑧=−5𝑧=−3𝑥−8
[6 −5 12 −1 13 0 1|
−17−5−8 ]
(3 ,0 ,1)
![Page 32: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/32.jpg)
Answer
Solve the system by: Your Choice
{ 𝑥+6 𝑦−2 𝑧=25𝑥−5 𝑦−3 𝑧=9
6 𝑥+ 𝑦+6 𝑧=−28
![Page 33: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/33.jpg)
Solve the system
{ 𝑥+6 𝑦−2 𝑧=25𝑥−5 𝑦−3 𝑧=9
6 𝑥+ 𝑦+6 𝑧=−28
[1 6 −21 −5 −36 1 6 | 25
9−28 ] (1 ,2 ,−6)
![Page 34: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/34.jpg)
-5 5
-5
5
x
y
Answer
Graph the solution to each inequality
7 𝑥−3 𝑦>−9
![Page 35: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/35.jpg)
-5 5
-5
5
x
y
Graph the solution to each inequality
7 𝑥−3 𝑦>−9
![Page 36: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/36.jpg)
-5 5
-5
5
x
y
Answer
Graph the solution to each inequality
{ 𝑥− 𝑦 ≤2𝑦<4 𝑥+1
![Page 37: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/37.jpg)
-5 5
-5
5
x
y
Graph the solution to each inequality
{ 𝑥− 𝑦 ≤2𝑦<4 𝑥+1
![Page 38: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/38.jpg)
Answer
Graph the solution to each inequality
{𝑦 ≥2|𝑥−3|−4
𝑦<− 23𝑥+1
-5 5
-5
5
x
y
![Page 39: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/39.jpg)
-5 5
-5
5
x
y
Graph the solution to each inequality
{𝑦 ≥2|𝑥−3|−4
𝑦<− 23𝑥+1
![Page 40: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/40.jpg)
-5 5
-5
5
x
y
Answer
Graph the feasible region and find the point that maximize the function:
{ 𝑦 ≥ 𝑥−2𝑥+2 𝑦 ≤8𝑦 ≥1𝑥≥0
![Page 41: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/41.jpg)
-5 5
-5
5
x
y
-5 5
-5
5
x
y
Graph the feasible region and find the point that maximizes the function:
{ 𝑦 ≥ 𝑥−2𝑥+2 𝑦 ≤8𝑦 ≥1𝑥≥0
(0, 1)
(0, 5)
(4, 2)
(3, 1)
![Page 42: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/42.jpg)
Answer
Graph the feasible region and find the point that maximizes the function:
{−𝑥+2 𝑦 ≤4𝑥+𝑦 ≤8𝑦 ≥1𝑥≥2
-1 10-1
10
x
y
![Page 43: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/43.jpg)
-1 10-1
10
x
y
Graph the feasible region and find the point that maximizes the function:
{−𝑥+2 𝑦 ≤4𝑥+𝑦 ≤8𝑦 ≥1𝑥≥2
-1 10-1
10
x
y
(2, 1)
(2, 2)
(5, 4)
(7, 1)
![Page 44: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/44.jpg)
Answer
The school that Danielle goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 7 senior citizen tickets and 3 child tickets for a total of $74. The school took in $135 on the second day by selling 14 senior citizen tickets and 5 child tickets. Write a system of equations to find the price of one senior citizen ticket and one child ticket?
![Page 45: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/45.jpg)
The school that Danielle goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 7 senior citizen tickets and 3 child tickets for a total of $74. The school took in $135 on the second day by selling 14 senior citizen tickets and 5 child tickets. Write a system of equations to find the price of one senior citizen ticket and one child ticket?
![Page 46: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/46.jpg)
Answer
Amanda and Eduardo each improved their yards by planting grass sod and shrubs. They bought their supplies from the same store. Amanda spent $83 on 7 ft² of grass sod and 3 shrubs. Eduardo spent $118 on 8 ft² of grass sod and 6 shrubs. Find the cost of one ft² of grass sod and the cost of one shrub.
Write a system of equation to solve the problem.
![Page 47: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/47.jpg)
Amanda and Eduardo each improved their yards by planting grass sod and shrubs. They bought their supplies from the same store. Amanda spent $83 on 7 ft² of grass sod and 3 shrubs. Eduardo spent $118 on 8 ft² of grass sod and 6 shrubs. Find the cost of one ft² of grass sod and the cost of one shrub.
Write a system of equation to solve the problem.
![Page 48: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/48.jpg)
Answer
Meg has three dogs – Skippy, Gizmo, and Chopper. The sum of the dogs’ weights is 148 pounds. If you add three times Skippy’s weight to Gizmo’s weight, the sum is 8 pounds less than Chopper’s weight. If you subtract one-third of Skippy’s weight from four times Gizmo’s weight, the result is equal to twice Chopper’s weight.Write a system of equations to find out how much each dog weighs? Then solve the system.
![Page 49: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/49.jpg)
Meg has three dogs – Skippy, Gizmo, and Chopper. The sum of the dogs’ weights is 148 pounds. If you add three times Skippy’s weight to Gizmo’s weight, the sum is 8 pounds less than Chopper’s weight. If you subtract one-third of Skippy’s weight from four times Gizmo’s weight, the result is equal to twice Chopper’s weight.Write a system of equations to find out how much each dog weighs? Then solve the system.
Skippy: 12 poundsGizmo: 46 poundsChopper: 90 pounds
![Page 50: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/50.jpg)
Answer
You manage a health food store and budget $80 to buy ingredients to make 30 pounds of trail mix. Peanuts cost $2.50 per pound, raisins cost $2.00 per pound and granola cost $4.00 per pound. If you use twice as many pounds of peanuts as raisins, how many pounds of each ingredient should you buy?
![Page 51: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/51.jpg)
You manage a health food store and budget $80 to buy ingredients to make 30 pounds of trail mix. Peanuts cost $2.50 per pound, raisins cost $2.00 per pound and granola cost $4.00 per pound. If you use twice as many pounds of peanuts as raisins, how many pounds of each ingredient should you buy?
{2.5𝑝+2𝑟+4𝑔=80 𝑝+𝑟 +𝑔=30𝑝=2𝑟
Peanuts (p): 16 poundsRaisins (r): 8 poundsGranola (g): 6 pounds
![Page 52: Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213.](https://reader035.fdocuments.in/reader035/viewer/2022081501/56649c9a5503460f949577db/html5/thumbnails/52.jpg)
Answer
You are making your summer movie plans and are working with following constraints:• It costs $8 to go to the movies at night.• It costs $5 to go to a matinee.• You want to go to at least as many night shows as matinees.• You want to spend at most $42What is the greatest number of movies you can see?
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You are making your summer movie plans and are working with following constraints:• It costs $8 to go to the movies at night.• It costs $5 to go to a matinee.• You want to go to at least as many night shows as matinees.• You want to spend at most $42What is the greatest number of movies you can see?
{8𝑛+5𝑚≤ 42𝑛≥𝑚𝑛≥0𝑚≥0
1 2 3 4 5 6 7
1
2
3
4
5
6
7
Matinee
Night
6 Movies:3 night, 3 matinee4 night, 2 matinee