# How to Evaluate Two Variables? (+FREE Worksheet!)

You can evaluate a mathematical expression with two variables when you have the values of the variables.

## Related Topics

- How to Translate Phrases into an Algebraic Statement
- How to Simplify Variable Expressions
- How to Simplify Polynomial Expressions
- How to Use the Distributive Property
- How to Evaluate One Variable

## Step by step guide to evaluating two variables

- To evaluate an algebraic expression, substitute a number for each variable and perform the arithmetic operations.

### Evaluating Two Variables – Example 1:

Solve this expression. \(4 \ (2a \ – \ b), \ a=2, \ b=\ – 1\)

**Solution:**

First use distributive property formula: \(𝑎(𝑏 + 𝑐)=𝑎𝑏 + 𝑎𝑐\)

\(4 \ (2a \ – \ b)= 8a \ – \ 4b\)

Now, substitute \(2\) for \(a\) , and \(- \ 1\) for \(b\), then:

\(4 \ (2a \ – \ b)= 8a \ – \ 4b= 8 \ (2) \ – \ 4 \ (- 1)=16 \ + \ 4=20 \)

### Evaluating Two Variables – Example 2:

Solve this expression. \(2x \ + \ 6y, x=1 \ , \ y=2\)

**Solution:**

First substitute \(1\) for \(x\), and \(2\) for \(y\) , then:

\(2x \ + \ 6 y =2 \ (1) \ + \ 6 \ (2)=2 \ + \ 12=14 \)

### Evaluating Two Variables – Example 3:

Solve this expression. \(-3x+5y ,x=2,y=-1\)

**Solution:**

First substitute \(2\) for \(x\), and \(-1\) for \(y \), then:

\( -3x+5y=-3(2)+5(-1)=-6-5=-11\)

### Evaluating Two Variables – Example 4:

Solve this expression. \(2(a-2b),a=-1,b=3\)

**Solution:**

First use distributive property formula: \(𝑎(𝑏 + 𝑐)=𝑎𝑏 + 𝑎𝑐\)

\( 2(a-2b)=2a-4b\)

Now, substitute \(-1\) for \(a\) , and \(3\) for \(b\) , then:

\( 2(a-2b)=2a-4b=2(-1)-4(3)= -2-12= -14 \)

## Exercises for Evaluating Two Variables

### Simplify each algebraic expression.

- \(\color{blue}{2x + 4y – 3 + 2, \\ x = 5, y = 3 } \\\)
- \(\color{blue}{(– \frac{12}{x}) + 1 + 5y, \\ x = 6, y = 8} \\ \)
- \(\color{blue}{(– 4) (– 2a – 2b), \\ a = 5, b = 3} \\ \)
- \(\color{blue}{10 + 3x + 7 – 2y, \\ x = 7, y = 6} \\ \)
- \(\color{blue}{9x + 2 – 4y, \\ x = 7, y = 5} \\ \)
- \(\color{blue}{6 + 3 (– 2x – 3y), \\ x = 9, y = 7} \\ \)

### Download Evaluating Two Variables Expressions Worksheet

## Answers

- \(\color{blue}{21}\)
- \(\color{blue}{39}\)
- \(\color{blue}{64}\)
- \(\color{blue}{26}\)
- \(\color{blue}{45}\)
- \(\color{blue}{-111}\)

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