IXL - Solve a system of equations by graphing: word problems (Algebra 1 practice)

Two tailors, Rosanne and Maggie, sit down to do some embroidery. Rosanne can embroider 3 shirts per hour, and Maggie can get through 5 shirts per hour. In addition, the tailors had previously finished some shirts. Rosanne has already completed 15 shirts, and Maggie has completed 5 shirts. Rosanne and Maggie decide to take a break when they have finished the same total number of shirts. How many shirts, in total, will each tailor have finished?

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

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

shirts

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question

Fred is going to send some flowers to his wife. Booneville Florist charges $2 per rose, plus $25 for the vase. Samir's Flowers, in contrast, charges $1 per rose and $30 for the vase. If Fred orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be?

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

dollars

solution

Start by writing a system of equations. Let

roses

and

dollars

The first equation is

The

-intercept

is 25. Plot the point

(

)

The slope is 2, which is the same as

Move up 10 and right 5 to find another point on the line.

Draw a line connecting them.

The second equation is

The

-intercept

is 30. Plot the point

(

)

The slope is 1, which is the same as

Move up 5 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

(

)

If the bouquet contains 5 roses, it will cost $35.

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Lesson: Systems of equations

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Not feeling ready yet? These can help:

N.8Write a linear function: word problems

O.2Solve a system of equations by graphing

Lesson: Systems of equations

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