GOZUNTA
Try it now
All courses Math I · A-REI.6 12 of 59
Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.

Solve a system by substitution when one variable is already isolated

Problem
Solve the system by substitution: y = 2x + 1, x + y = 10.
Your answer
With a free account

Take your practice with you.

Sign in on the web or in the iPhone and iPad app to use the same saved sessions and results.

Create a free account
With paid access

Build sessions from the full problem bank.

Choose the objective you need and make a learning session using all of its available problem types and variants.

Compare plans

Hint

Substitute 2x + 1 for y in the equation x + y = 10.

Substitution works by replacing one variable with an equivalent expression from the other equation.

Solution walkthrough

01

Substitute for y

\[x~+~y~=~10~\Rightarrow~x~+~(2x~+~1)~=~10\]

Because y = 2x + 1, you can replace y with 2x + 1 in the second equation.

02

Solve for x

\[x~+~2x~+~1~=~10~\Rightarrow~3x~=~9~\Rightarrow~x~=~3\]

Combine like terms, subtract 1, and divide by 3.

03

Substitute back to find y

\[y~=~2x~+~1~\Rightarrow~y~=~2(3)~+~1~=~7\]

Use x = 3 in the expression for y.

04

State the solution

\[(x,~y)~=~(3,~7)\]

So the ordered-pair solution to the system is (3, 7).

+

Another way

  1. You can substitute x = (y - 1)/2 into x + y = 10 instead, but using y = 2x + 1 is the cleaner starting point.

!

Common mistake

A common mistake is to replace y with 2x and forget the +1, which changes the equation.