IXL | Solve a system of equations using substitution

Solve using substitution.

x − 4y = 17

y = ^–5

(, )

ref_doc_title.

Learn with an example

question

Solve using substitution.

^–x + 3y = ^–15

x = ^–3

(, )

key idea

To solve using substitution, follow these four steps:

Step 1: Isolate a variable.

Step 2: Plug the result of Step 1 into the other equation and solve for one variable.

Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.

Step 4: State the solution.

solution

Use substitution to solve the system of equations:

^–x + 3y = ^–15

x = ^–3

Step 1: Isolate a variable.

The variable x is already isolated in the second equation.

Step 2: Plug the result of Step 1 into the other equation and solve for one variable.

Plug x = ^–3 into the other equation, ^–x + 3y = ^–15, and find the value of y.

^–x + 3y

^–15

Plug in x = ^–3

3 + 3y

^–15

Plug in x = ^–3

Subtract 3 from both sides

^–18

Subtract 3 from both sides

Divide both sides by 3

^–6

Divide both sides by 3

Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.

The second equation already shows that x = ^–3, so it is not necessary to plug in and solve for x.

Step 4: State the solution.

Since x = ^–3 and y = ^–6, the solution is (^–3, ^–6).

Looking for more? Try these:

Lesson: Systems of equations

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	04

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

M.15Solve equations using the distributive property

GG.1Is (x, y) a solution to the system of equations?

Lesson: Systems of equations

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!