IXL - Solve a system of equations using substitution: word problems (Precalculus practice)

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

Franco works in the shipping department of a toy factory that makes radio-controlled helicopters. Small helicopters weigh 1 kilogram each, and are shipped in a container that weighs 9 kilograms. Large ones, on the other hand, weigh 2 kilograms apiece, and are shipped in a container that weighs 7 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? How many helicopters would fit in either container?

The shipping weight of a full container of either size will be kilograms if it holds helicopters.

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Learn with an example

question

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

Abby and her sister Mia are making baby blankets to sell at a boutique. Abby has already completed 5 blankets and can finish 8 more blankets per day. Mia has already completed 6 blankets and can finish 7 more blankets per day. At some point, they will have completed the same number of blankets. How many blankets will each woman have made? How long will that take?

Each woman will have finished blankets in days.

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 days, and let y represent blankets.

y = 8x + 5

y = 7x + 6

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 = 8x + 5 into the other equation, y = 7x + 6, and find the value of x.

7x + 6

Plug in y = 8x + 5

8x + 5

7x + 6

Plug in y = 8x + 5

Subtract 7x from both sides

x + 5

Subtract 7x from both sides

Subtract 5 from both sides

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 = 8x + 5. Then find the value of y.

8x + 5

Plug in x = 1

8(1) + 5

Plug in x = 1

Multiply

8 + 5

Multiply

Add

Step 4: State the solution.

Since x = 1 and y = 13, the solution is (1, 13).

Each woman will have finished 13 blankets in 1 day.

Looking for more? Try these:

Lesson: Systems of equations

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Lesson: Systems of equations

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