Solve Systems of Linear Equations by SubstitutionHonors Math – Grade 8

One way to find an exact solution to a system of linear equations is to use substitution.

{ 𝑦=3 𝑥+22𝑥+2 𝑦=28

Substitution is best used when one of the equations in the system is solved for either x or y.

To use this method, solve one of the equations (if needed) for one of the variables and then substitute for the variable into the other equation.

Let’s take a closer look…

Solve each system of equations by using the substitution method.

{ 𝑦=3 𝑥+22𝑥+2 𝑦=28

This equation is solved for y. Use Substitution.

Use this equation and substitute for y.

2 𝑥+2 𝑦=28Plug in and solve for x. To find the corresponding y-value, substitute

for x into the first equation and solve.

𝑦=3 𝑥+2

Solve each system of equations by using the substitution method.

{2𝑥+7 𝑦=3𝑥=1−4 𝑦 This equation is solved for

x. Use Substitution.

Use this equation and substitute for x.

2 𝑥+7 𝑦=3Plug in and solve for y. To find the corresponding x-value, substitute

for y into the second equation and solve.

𝑥=1−4 𝑦

Solve each system of equations by using the substitution method.

{ 𝑥+4 𝑦=72𝑥−2 𝑦=9

Since the coefficient of x is 1. Solve for x.

Use this equation and substitute for x.

2 𝑥−2 𝑦=9Plug in and solve for y. To find the corresponding x-value, substitute

for y into the second equation and solve.

𝑥=7−4 𝑦

Sometimes you need to transform one of the equations to solve for one of the variables. The equation that is easier to solve is the one with a variable that has a coefficient of 1.

Solve each system of equations by using the substitution method.

{ 2 𝑥− 𝑦=−4−3 𝑥+𝑦=−9 Since the coefficient of y is

1. Solve for y.

Use this equation and substitute for y.

2 𝑥− 𝑦=−9Plug in and solve for y. To find the corresponding y-value, substitute

for x into the second equation and solve.

y=3 𝑥−9

Sometimes you need to transform one of the equations to solve for one of the variables. The equation that is easier to solve is the one with a variable that has a coefficient of 1.

Solve each system of equations by using the substitution method.

{ 𝑦=3 𝑥+26 𝑥−2 𝑦=−4

This equation is solved for y. Use Substitution.

Use this equation and substitute for y.

6 𝑥−2 𝑦=−4Plug in and solve for x.

The statement is a reflexive statement. This means that there are infinitely many solutions.

Solve each system of equations by using the substitution method.

{𝑦=2 𝑥−32𝑥−𝑦=8

This equation is solved for y. Use Substitution.

Use this equation and substitute for y.

2 𝑥− 𝑦=8Plug in and solve for x.

This results in a false statement. There is no solution to the system of equations. The lines are parallel.