Intro to Elimination

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph
• Don't touch
• Intersect
• Exist

You can solve systems using these methods:

• graphing, substitution, and elimination

• rearranging, thinking, and guessing

• only by graphing

• only by elimination

Which variable would be easiest to eliminate?

4x + 8y = 20

−4x + 2y = −30

• x because they have equal coefficients but opposite sign

• y because they have equal coefficients but opposite sign

Which variable would be easiest to eliminate?

-3x - 5y = 1

6x + 5y = -10

• x because they have equal coefficients but opposite sign

• y because they have equal coefficients but opposite sign

Which variable would be easiest to eliminate?

2x + 2y = -2

3x - 2y = 12

• you cannot solve this using eliminiation

• x because they have equal coefficients but opposite sign

• y because they have equal coefficients but opposite sign

Which variables & coefficients eliminate?

x + 6y = 20

-x - 3y = -11

• 20 and -11

• x and - x

• 6y and -3y

• cannot be solved using elimination

What is the resulting equation after adding the 2 equations?

5x - 4y = 11

5x + 4y = -14

• 5x = -3

• 10y = -3

• 10x = -3

• 10x = -25

What is the resulting equation after adding the 2 equations?

x + y = 11

-x + 4y = 14

• 2x + 5y=25

• 5y = 3

• 5y = 25

What could we multiply the 1st equation by to eliminate the x variable?

x + y = 11

3x - 4y = -2

• 3

• 4

• -3

• -4

What could we multiply the 1st equation by to eliminate the y variable?

x + y = 11

3x - 4y = -2

• 3

• 4

• -3

• -4