9.4 -- Solving systems by elimination

9.4 -- Solving systems by elimination

opposites = zero

•  $-5x\ +5x=0$  

•  $y+-y=0$  

Weird Rules

• If EVERYTHING cancels out, there are infinite solutions

   $\left\{3x-2y=4\right\}\left\{-3x+2y=-4\right\}$  

• If you lose both variables, there is NO solution  $\left\{x-y=3\right\}\left\{-x+y=7\right\}$  

"Making" Opposites

• Multiply EVERYTHING in one equation in order to make an opposite pair

• Multiply either the top or the bottom equation by -1 to make an opposite pair with 3x and -3x

Multiple Choice

How could we make an opposite pair from these equations?

• Multiply the top equation by 2

• Multiply the bottom equation by -2

• Multiply the bottom equation by 6

• Multiply the top equation by -2

Fill in the Blanks