Variable Substitution

Lesson 5.3: Solve Systems using Substitution

By Reed Carbone

Definition:

​Variable: A variable is a placeholder for a number we do not know yet.

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In this lesson, we are going to use variables to hold the place for entire expressions.​

Subject | Subject

Some text here about the topic of discussion

3x - y = 7

2x + y = 8​

How to solve system of equations using substitution:​

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.

Example:​

x = 8y - 4

x + 8y = 6​

Multiple Choice

What is the solution to the system of equations?

y = 3x - 10

3x + 2y = 16

• (2,4)

• (4,2)

• (3,8)

• (2,11)

​Example:

​Pedro has 276 more hits than Ricky. Use substitution to solve the system of equations to find how many hits Pedro, p, and Ricky, r, have recorded. The total combined hits is 2,666.

Multiple Choice

Jake buys a fruit smoothie and a protein bar for $5.90. Kobe buys 2 fruit smoothies and 4 protein bars for $16.80. Write a system of equations that can be used to find the price of each item individually. (Use s for smoothies and p for protein bars.)

• s = 5.90 + p

  p = 16.80 + s

• s + p = 5.90

  s + p = 16.80

• s + p = 5.90

  2s + 4p = 16.80

• 2s + 4p = 5.90

  s + p = 16.80

Try it out:​

6x - 2y = -6

11 = y - 5x​

​Step 1: Solve an equation for a variable.

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Step 2: Substitute that variable into your other equation.

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​Step 3: Solve the equation for your variable.

Step 4: Substitute your solution into the original equation.​

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Multiple Choice

What is the solution to the system of equations?

5x + y = -24

x + 3y = -2

• (-5,-1)

• (5,1)

• (-5,1)

• (5,-1)

Multiple Choice

Solve the previous system of equations to determine how much a protein bar and a smoothie cost.

s + p = 5.90

2s + 4p = 16.80

• s = 3.40

  p = 2.50

• s= 2.50

  p = 3.40

• s = 5.20

  p = 2.20

• s = 2.20

  p = 5.20

Conclusion: Write two complete sentences about what you learned.​