Unit 5 - Solving Systems by Elimination (Simple)

What would be the first step in finding the solution with elimination?

4x + 3y = 1

x - 3y = -11

• cross out the 3y and -3y

• cross out the 4x and x

• change all the signs of the second equation

• add 1 and -11

4x +  8y = 20
-4x + 2y = -30
Which variable will be eliminated?

• The  x

• The  y

• The  z

• The unknown

Which variable will be eliminated?

• x

• y

Solve by elimination:

4x + 9y = 28

-4x - y = -28

• (-7 , 0)

• (6 , 0)

• (-6 , 0)

• (7 , 0)

Solve by elimination: 7x + y = -9 -3x - y = 5

• No solution

• (1 , 8)

• (-2 , -3)

• (-1 , -2)

Solve by elimination:
x + 9y = 8
-6x - 9y = -3

• (1,-1)

• (1,1)

• (-1,1)

• (-1,-1)

Solve by elimination:

x + y = 10

-6x - y = 15

• No solution

• ( 5 , -15)

• (0 , 5)

• (-5 , 15)

Solve by elimination:

3x + 7y = 23

-3x - 7y = -17

• No solution

• All Real Numbers

• (-3 , 3)

• (3 , 3)

Answer explanation

When all the variables cancel out and the remaining equality is a FALSE statement, there is no solution.

Example:

7 = 0 is a FALSE statement, therefore the answer is

NO SOLUTION

A system of two parallel lines will have how many solutions?

• One Solution
• Two Solutions
• No Solution
• Infinite Solutions

A system of two identical (overlapping) lines will have how many solutions?

• One Solution
• Two Solutions
• No Solution
• Infinite Solutions