IXL | Solve a system of equations using substitution: word problems

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Toby and Grace both went bowling last weekend, but not together. Toby went during open bowling time, paying $2 for shoe rental and $3 per hour. Grace went on family night, when each hour was $1 and shoe rental was $16. As it turned out, they played for the same number of hours and spent the same amount. How many hours did each one bowl? How much did each one spend?

Toby and Grace each bowled for hours and spent $.

ref_doc_title.

Learn with an example

question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Mitchell went to play miniature golf on Monday, when it cost $8 to rent the club and ball, plus $1 per game. Jessica went Thursday, paying $5 per game, plus rental fees of $4. By coincidence, they played the same number of games for the same total cost. How many games did each one play? How much did each one spend?

Mitchell and Jessica each played games and spent $.

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

Before you can solve, you must write a system of equations. Let x represent games, and let y represent dollars.

y = x + 8

y = 5x + 4

Now use substitution to solve the system of equations.

Step 1: Isolate a variable.

The variable y is already isolated in the first equation.

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

Plug y = x + 8 into the other equation, y = 5x + 4, and find the value of x.

5x + 4

Plug in y = x + 8

x + 8

5x + 4

Plug in y = x + 8

Subtract 5x from both sides

^–4x + 8

Subtract 5x from both sides

Subtract 8 from both sides

^–4x

^–4

Subtract 8 from both sides

Divide both sides by ^–4

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

Take the result of Step 2, x = 1, and plug it into one of the original equations, such as y = x + 8. Then find the value of y.

x + 8

Plug in x = 1

1 + 8

Plug in x = 1

Add

Step 4: State the solution.

Since x = 1 and y = 9, the solution is (1, 9).

Mitchell and Jessica each played 1 game and spent $9.

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:

GG.8Solve a system of equations using substitution

CC.11Write linear functions: word problems

Lesson: Systems of equations

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!