Variable Substitution

Substitution Review

By Reed Carbone

​Goal: When solving with substitution, we want to solve for a variable and then replace it in the equation.

​Step 1: Solve one of your equations for a certain variable (either x or y it doesn't matter)

Step 2: Substitute the expression you find into your other equation.

Step 3: Combine like terms until you can solve for your remaining variable.

Step 4: Plug the value you find for your variable into your original equation to solve for the final ​variable.

​x + 5y = 0

25y = -5x​

One day, 481 people used a swimming pool. The prices were $1.25 for children and $2.25 for adults. The receipts for admission totaled $865.25. How many children and how many adults swam at the pool that day?​

Multiple Choice

6x - 2y = -6

11 = y - 5x

• Infinitely Many Solutions

• No Solutions

• (-9,-4)

• (-4,-9)

Multiple Choice

y = 3x - 10

3x + 2y = 16

• Infinitely Many Solutions

• No Solutions

• (4,2)

• (2,4)

Multiple Choice

x = 8y - 4

x + 8y = 6

• Infinitely Many Solutions

• No Solutions

• $$\left(1,\frac{5}{8}\right)$$  

• $$\left(\frac{5}{8},1\right)$$  

Multiple Choice

Pedro has 276 more hits than Ricky. They have a total combined hits of 2,666. How many hits did each of them have?

• Pedro 1,471

  Ricky 1,195

• Pedro 1,195

  Ricky 1,471

• Pedro 1,252

  Ricky 1,414

• Pedro 1,414

  Ricky 1,252

Multiple Choice

Tickets to a play are $3 for students and $8 for adults. On opening night, $1,000 was collected and 150 tickets were sold. How many adults and students attended the play?

• 50 Adults

  100 Students

• 100 Adults

  50 Students

• 40 Adults

  110 Students

• 110 Adults

  40 Students