09+-+Sec+7.2

= **7.2 Solving Linear Equations by Substitution** =

By:Alex Murfin

= **EXPLANATION** = - Substitution is the process of replacing a variable with a value or number to find the final answer of the expression. - Solve one of the equations for one of its variables -Substitute this expression into the other equation and solve for the other variable -Check the solution pair in each of the original equations

Substitution Game

//__**Red= Answers**__//
1. -x+y= 1 and 2x + y = -2

y = x+1

2x + ( x + 1) = -2

3x + 1 = -2 -1 -1 3x = -3

3
 * x = -1 **

y = -1+ 1

**y = 0** The solution is ** ( -1, 0) **

2. 2x + 2y = 3 and x - 4y = -1 . +4y +4y

x = 4y + -1

2( 4y - 1) + 2y = 3

10y - 2 = 3 +2 +2 10y=5

10
 * y = 1/2 **

x= 4(1/2) -1 2 -1 =1 x= 1 The solution is ** ( 1, 1/2) **

3. 2x = 5 and x + y = 1

2x =5

2 x = 5/2

x+y=1 -x -x

y = -x + 1

y = -5/2 + 2/2 = -3/2

y= -3/2

The solution is ( 5/2, -3/2)

Practice problems without solutions

Solve the System

1. x-y=0, 2x+y=0

2. x-2y=0, 3x-y=0

= =