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

Colleen works in the shipping department of a toy factory that makes radio-controlled helicopters. Small helicopters weigh 2 kilograms each, and are shipped in a container that weighs 20 kilograms. Large ones, on the other hand, weigh 4 kilograms apiece, and are shipped in a container that weighs 10 kilograms. If these boxes can hold a certain number of helicopters each, all of the packed containers will have the same shipping weight. What would the total weight be?

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

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

kilograms

ref_doc_title.

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question

Eliana wants to buy a charm bracelet. Georgetown Fine Jewelry charges $4 per charm, plus $60 for the bracelet. Pittman Jewelers, in contrast, charges $9 per charm and $10 for the bracelet. If Eliana wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. What would the total cost of the bracelet be?

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

dollars

solution

Start by writing a system of equations. Let

charms

and

dollars

The first equation is

The

-intercept

is 60. Plot the point

(

)

The slope is 4, which is the same as

Move up 20 and right 5 to find another point on the line.

Draw a line connecting them.

The second equation is

The

-intercept

is 10. Plot the point

(

)

The slope is 9, which is the same as

Move up 90 and right 10 to find another point on the line.

Draw a line connecting them.

Finally, identify the point of intersection.

The lines intersect at

(

100

)

If Eliana adds 10 charms to her bracelet, it will cost $100 at either shop.

Looking for more? Try these:

Lesson: Systems of equations

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Not feeling ready yet? These can help:

N.1Solve a system of equations by graphing

N.8Write a linear function: word problems

Lesson: Systems of equations

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