Systems of Equations

Learn how to solve two equations at the same time.

What You'll Learn:

Lesson 1:

Substitution

Example:

y = x + 2

2x + y = 8

2x + (x + 2) = 8

3x + 2 = 8

x = 2

2x + y = 8

4 + y = 8

y = 4 (2, 4)

Lesson 2:

Elimination

Add/or subtract to eliminate variable.

Example: Add or subtract to eliminate variable

2x + 2y = 10

x-2y= 2

3x + 0y = 12

3x= 12

x = 4

Substitute 4

2(4) + 2y = 10

8 + 2y = 10

2y = 2

y = 1

Practice Problems

Easy

y = x + 1

x + y = 7

Medium

3x + 2y = 4

2x + 3y = 1

Challenge

Two friends spent a total of $30 on lunch. One spent $6 more than the other. How much did each person spend?

Common Mistakes to Avoid

Quick Recap:

Solution = the (x, y)

that works in

BOTH equations

The point where the two lines intersect.

Answer Key:

Easy: (3, 4)

Medium: (2, -1)

Challenge: One friend spent $18, the other spent $12

Want step-by-step help and more practice?