Algebra 1 Common Core Student Edition, Grade 8-9

Check y = 3x x + y = - 32

—24 — 3 ( —8) —8 + ( —24) — —32

—24 = —24 t / —32 = —32 ^

% Got It? 1. W hat is th e solution of th e system? Use substitution, y = 2x + 7

Check your answer. y = x — 1

Which variableIJUfl
should you solve for?
If one e q u a tio n has
a v a ria b le w ith a
coefficient of 1 or - 1 ,
solve for that variable.
It is g e n e ra lly easier to
solve fo r a va ria b le w ith
a c o e ffic ie n t o f 1 or - 1.

To use substitution to solve a system of equations, one of th e eq u atio n s m u st be solved

for a variable.

Problem 2 Solving for a Variable and Using Substitution

What is the solution of the system? Use substitution. 3y + 4x = 14

— 2 x + y = - 3

Solve one o f the equations fo r one o f the

variables. Then use th e substitution method

to fin d th e solution o f the system.

N e ith e r e q u a tio n is solved

for one o f the variables.

The s o lu tio n o f th e

system

Step 1 Solve one of th e eq u atio n s for one of th e variables.

—2 x + y = -3 Write the second equation.

• 2x + y + 2 x = — 3 + 2x Add 2x to each side,
  y = 2x - 3 Simplify.
  Step 2 Substitute 2 x - 3 for y in th e o th er e q u a tio n a n d solve for x.
  3y + 4x = 14 Write the first equation.
  3(2x - 3) + 4x = 14 Substitute 2x - 3 for y. Use parentheses.
  6 x — 9 + 4x = 14 Distributive Property
  lO x = 23 Add 9 to each side. Simplify,
  x = 2.3 Divide each side by 10.
  Step 3 Substitute 2.3 for x in eith er eq u a tio n an d solve for y.
  -2 x + y = -3
  -2 (2 .3 ) + y = - 3
  -4 .6 + y = - 3
  y= 1.6
  The solution is (2 .3 ,1 .6 ).

Write either equation.

Substitute 2.3 forx.

Simplify.

Add 4.6 to each side.

Got It? 2. a. W hat is th e solution of th e system? Use substitution. 6y + 5x = 8

x + 3y = — 7

b. Reasoning In your first step in p a rt (a), w hich variable did you solve for?

W hich eq u a tio n did you use to solve for th e variable?

PowerAlgebra.com Lesso n 6- 2 So l vi n g Syst em s Usin g Su b st i t u t i o n^373