Solving Linear Systems by Substitution - Flagler County Schools

7.2
Solving Linear Systems
by Substitution
Goals p Use substitution to solve a linear system.
p Model a real-life situation using a linear system.
SOLVING A LINEAR SYSTEM BY SUBSTITUTION
Step 1 Solve one of the equations for one of its variables .
Step 2 Substitute the expression from Step 1 into the other
equation and solve for the other variable .
Step 3 Substitute the value from Step 2 into the revised
equation from Step 1 and solve.
Step 4 Check the solution in each of the original equations.
Example 1 Choosing an Equation to Solve
Tell which equation you would use to isolate a variable. Explain your
reasoning.
a. 6x y 5 Equation 1 b. 5c 2d 1 Equation 1
2x 3y 10 Equation 2 c 3d 0 Equation 2
Solution
a. It would be easiest to isolate y in Equation 1 because the
variable has a coefficient of 1 .
b. It would be easiest to isolate c in Equation 2 because the
variable has a coefficient of 1 .
Lesson 7.2 • Algebra 1 Notetaking Guide 137

138 Algebra 1 Notetaking Guide • Chapter 7
Example 2 The Substitution Method
Solve the linear system.
2x 5y 13 Equation 1
x 3y 1 Equation 2
Solution
1. Solve for x in Equation 2 because it is easy to isolate x.
x 3y 1 Revised Equation 2
2. Substitute 3y 1 for x in Equation 1 and solve for y.
2x 5y 13 Write Equation 1.
2( 3y 1 ) 5y 13 Substitute for x.
6y 2 5y 13 Distribute.
11y 2 13 Simplify.
11y 11 Add 2 to each side.
y 1 Solve for y.
3. To find the value of x, substitute 1 for y in the revised
Equation 2 and solve for x.
x 3y 1 Write revised Equation 2.
x 3(1) 1 Substitute for y.
x 4 Simplify.
4. Check that ( 4 , 1 ) is a solution by substituting 4 for
x and 1 for y in each of the original equations.
Equation 1 Equation 2
2x 5y 13 x 3y 1
2( 4 ) 5( 1 ) 13 4 3( 1 ) 1
8 5 13 4 3 1
13 13 1 1
Answer The solution is ( 4 , 1 ).

Checkpoint Tell which equation you would use to isolate a
variable. Explain your reasoning.
1. x 2y 0 2. 4x 2y 10
x 8y 5 7xy12 I would isolate x in the I would isolate y in the
first equation because it second equation because
is easy to do so and the it is easier to do so than
value is easy to substitute to isolate y in the first
in the other equation. equation or x in either
equation.
Use the substitution method to solve the linear system.
3. y x 1 4. y 5x 3
x 5y 15 3x 2y 8
(5, 4) (2, 7)
Lesson 7.2 • Algebra 1 Notetaking Guide 139