3-2Solving Systems Algebraically:

Substitution Method

Objective:

I can solve a system of equations using the substitution method.

Substitution Method

Steps:

1. Solve one equation for one of the variables.

2. Substitute the expression for the variable into the other equation and solve.

3. Substitute this value into one of the original equations and solve.

4. CHECK YOUR ANSWERS: Substitute both values into both equations to be sure they work.

Examples

33

72

xy

xy

34

954

xy

yx

83

9

yx

xy

72 x 33 x

375 x

105 x

2x7 2 y x)2( 3

7)2(23 3)2(33

)3,2(

954 yx9) (54 x 34 x

915204 xx

91524 x2424 x1x

3 4 y x)1( 1

)1,1(

9 xy9) ( y 83 y

983 yy984 y14 y4/1y

8)25.0(3 x

75.8x

)25.0,75.8(

y

Examples

32

823

yx

yx

867 x

147 x

2x3 2 y x)2( 1

)1,2(

32 yx

yx 32

yx 32

823 yx8) (23 x 32 x

8643 xx

Variables:

An online music company offers 15 downloads for $19.75 and 40 downloads for $43.50. Each price includes the same one-time registration fee.What is the cost of each download and the registration fee?

d = download cost f = Registration fee75.1915 fd

50.4340 fd

Download cost = $0.95

Registration fee = $5.50

df 4050.43

75.19)4050.43(15 dd

75.2325 d

95.0d

)95.0(4050.43 f

50.5f

p. 146:10-21 [Don’t forget to check your answers!!]

3-2 Day 2

Solving Systems Algebraically:Elimination Method

Objective:I can solve a system of equations using the

elimination method.

Elimination MethodSteps:1. Equations need to be written in standard form.2. Multiply one or both equations so that one variable

in each equation has the same coefficient but opposite signs.

3. Add the two equations together to eliminate one variable and solve.

4. Substitute this value into one of the original equations and solve.

5. CHECK YOUR ANSWERS

) (1) (7

Examples

x6 18

3x

93 2 yx)3(

936 y33 y1y

)1,3(

y3 00y

2 52 x y)0(

22 x1x

)0,1(

6

947

yx

yx

y11 333y

9 47 x y)3(

9127 x

217 x3x

)3,3(

947 yx

934

932

yx

yx

4277 yx222 yx

252

222

yx

yx

252 yx

) (5) (2

1622

035

yx

yx

Examples

y16 805y

0 35 x y )5(

0155 x

155 x3x

)5,3(

0610 yx

) (3) (4

1343

2935

yx

yx

x11 77

7x

293 5 yx )7(

29335 y

63 y2y

)2,7(

801010 yx 39129 yx1161220 yx

Solve the following systems

53

53

yx

yx

00

Dependent system.

Infinitely many solutions.

1064

664

yx

yx

160

Inconsistent system.

No solutions.

18312

64

yx

yx

00

18312

18312

yx

yx

Dependent system.

Infinitely many solutions.

You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save $100 per week and your friend saves $75 per week. When the vacation time comes, you have $1,150 and your friend has $1,000. How much did you start with and for how many weeks did you save?x = Amount you started with

y = # of weeks you saved

1150100 yx)100075(1 yx

15025 y

6y1000)6(75 x

550$x

p. 146:23-53 odds, 57, 58