Question

To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 2x-4y=6 -3x+3y=12

Answer 1

x = -11, y = -7

Explanation:

`\left\{\begin{array}{ccc}2x-4y=6&\text{multiply both sides by 3}\\-3x+3y=12&\text{multiply both sides by 4}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}6x-12y=18\\-12x+12y=48\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-6x=66\qquad\text{divide both sides by (-6)}\\.\qquad(-6x)/(-6)=(66)/(-6)\\.\qquad \boxed{x=-11}`

`\text{Put it to (2):}\\\\-3(-11)+3y=12\\33+3y=12\qquad\text{subtract 33 from both sides}\\3y=-21\qquad\text{divide both sides by 3}\\(3y)/(3)=(-21)/(3)\\y=-7`