BY GRAPHING Y = 2X + 1 Y = -X + 4 (1,3) IS THE SOLUTION.
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Transcript of BY GRAPHING Y = 2X + 1 Y = -X + 4 (1,3) IS THE SOLUTION.
BY GRAPHING
Y = 2X + 1
Y = -X + 4
(1,3) IS THE SOLUTION
Graphing is not the only way to solve a system of equations. It is not really the best way because it has to be graphed perfectly and some answers are not integers.
SOOOOWe need to learn another way!!!!
Solve: by ELIMINATION
x + y = 12-x + 3y = -8
We need to eliminate (get rid of) a variable.
The x’s will be the easiest. So, we will add the two equations.
4y = 4 Divide by 4
y = 1
THEN----
Like variables must be lined under each other.
X +Y = 12
(11,1)
Substitute your answer into either original equation and solve for the second variable.
Answer
Now check our answers in both equations------
x + 1 = 12 -1 -1 x = 11
X + Y =12
11 + 1 = 12
12 = 12
-x + 3y = -8
-11 + 3(1) = -8
-11 + 3 = -8
-8 = -8
Solve: by ELIMINATION
5x - 4y = -21-2x + 4y = 18
We need to eliminate (get rid of) a variable.
The y’s be will the easiest.So, we will add the two equations.
3x = -3 Divide by 3
x = -1
THEN----
Like variables must be lined under each other.
5X - 4Y = -21
(-1, 4)
Substitute your answer into either original equation and solve for the second variable.
Answer
Now check our answers in both equations------
5(-1) – 4y = -21 -5 – 4y = -21
5 5-4y = -16
y = 4
5x - 4y = -215(-1) – 4(4) = -21
-5 - 16 = -21-21 = -21
-2x + 4y = 18
-2(-1) + 4(4) = 18
2 + 16 = 18
18 = 18
Solve: by ELIMINATION
2x + 7y = 315x - 7y = - 45
We need to eliminate (get rid of) a variable.
The y’s will be the easiest. So, we will add the two equations.
7x = -14 Divide by 7
x = -2
THEN----
Like variables must be lined under each other.
2X + 7Y = 31
(-2, 5)
Substitute your answer into either original equation and solve for the second variable.
Answer
Now check our answers in both equations------
2(-2) + 7y = 31 -4 + 7y = 31
4 47y = 35
y = 5
2x + 7y = 312(-2) + 7(5) = 31
-4 + 35 = 3131 = 31
5x – 7y = - 45
5(-2) - 7(5) = - 45
-10 - 35 = - 45
- 45 =- 45
Solve: by ELIMINATION
x + y = 30 x + 7y = 6
We need to eliminate (get rid of) a variable.
To simply add this time will not eliminate a variable. If one of the x’s was negative, it would be eliminated when we add. So we will multiply one equation by a – 1.
Like variables must be lined under each other.
X + Y = 30
X + 7Y = 6( ) -1
X + Y = 30
-X – 7Y = - 6
Now add the two equations and solve.
-6Y = 24
- 6 - 6
Y = - 4
THEN----
X + Y = 30
(34, - 4)
Substitute your answer into either original equation and solve for the second variable.
Answer
Now check our answers in both equations------
X + - 4 = 30 4 4
X = 34
x + y = 3034 + - 4 = 30
30 = 30
x + 7y = 6
34 + 7(- 4) = 6
34 - 28 = 6
6 = 6
Solve: by ELIMINATION
x + y = 4 2x + 3y = 9
We need to eliminate (get rid of) a variable.
To simply add this time will not eliminate a variable. If there was a –2x in the 1st equation, the x’s would be eliminated when we add. So we will multiply the 1st equation by a – 2.
Like variables must be lined under each other.
X + Y = 4
2X + 3Y = 9
-2X - 2 Y = - 8
2X + 3Y = 9
Now add the two equations and solve.
Y = 1
THEN----
( ) -2
(3,1)
Substitute your answer into either original equation and solve for the second variable.
Answer
Now check our answers in both equations------
X + Y = 4
X + 1 = 4
- 1 -1X = 3
x + y = 43 + 1 = 4 4 = 4
2x + 3y = 9
2(3) + 3(1) = 9
6 + 3 = 9
9 = 9
