IXL | Solve a system of equations by graphing: word problems

Wanda wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Wanda can pay $35 per month, plus $3 for each group class she attends. Alternately, she can get the second membership plan and pay $15 per month plus $7 per class. If Wanda attends a certain number of classes in a month, the two membership plans end up costing the same total amount. What is that total amount?

Write a system of equations, graph them, and type the solution.

x-axis, Classes, y-axis, Cost. Coordinate plane graph with 1 quadrants, x-axis coordinates from 0 to 10, y-axis coordinates from 0 to 50.

dollars

ref_doc_title.

Learn with an example

question

Roy just became a personal trainer and is finalizing his pricing plans. One plan is to charge $100 for the initial consultation and then $80 per session. Another plan is to charge $50 for the consultation and $90 per session. Roy realizes that the two plans have the same cost for a certain number of sessions. How many sessions is that?

Write a system of equations, graph them, and type the solution.

sessions

solution

Start by writing a system of equations. Let

sessions

and

dollars

100

The first equation is

100

The

-intercept

is 100. Plot the point

(

100

)

The slope is 80, which is the same as

400

Move up 400 and right 5 to find another point on the line.

Draw a line connecting them.

The second equation is

The

-intercept

is 50. Plot the point

(

)

The slope is 90, which is the same as

450

Move up 450 and right 5 to find another point on the line.

Draw a line connecting them.

Finally, identify the point of intersection.

The lines intersect at

(

500

)

For 5

sessions,

the cost is $500 on either plan.

Looking for more? Try these:

Lesson: Systems of equations

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Lesson: Systems of equations

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