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

Kinsley is making greeting cards, which she will sell by the box at an arts fair. She paid $30 for a booth at the fair, and the materials for each box of cards cost $4. She will sell the cards for $10 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How much will the sales and expenditures be?

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

x-axis, Boxes of cards, y-axis, Dollars ($). Coordinate plane graph with 1 quadrants, x-axis coordinates from 0 to 10, y-axis coordinates from 0 to 100.

dollars

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Learn with an example

question

Band students are tested on, and required to pass, a certain number of scales during the year. As of today, Olivia has passed 8 scales, whereas her friend Tristan has passed 4 of them. Going forward, Olivia has committed to passing 1 scale per week, and Tristan has committed to passing 3 per week. At some point soon, the two friends will have passed the same number of scales. How many scales will that be?

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

scales

solution

Start by writing a system of equations. Let

weeks

and

scales

The first equation is

The

-intercept

is 8. Plot the point

(

)

The slope is 1. Move up 1 and right 1 to find another point on the line.

Draw a line connecting them.

The second equation is

The

-intercept

is 4. Plot the point

(

)

The slope is 3. Move up 3 and right 1 to find another point on the line.

Draw a line connecting them.

Finally, identify the point of intersection.

The lines intersect at

(

)

In 2 weeks, the friends will each have passed 10

scales.

Looking for more? Try these:

Lesson: Systems of equations

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Work it out

Not feeling ready yet? These can help:

CC.11Write linear functions: word problems

GG.2Solve a system of equations by graphing

Lesson: Systems of equations

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