Question

Eliminate the x and y

Answer 1

Step-by-step explanation:

Eliminate the x:

$\left\{\begin{array}{ccc}x-2y=6\\3x+y=4\end{array}\right\\\\\text{Multiply by (-3)}\\\\\left\{\begin{array}{ccc}-3(x-2y)=(-3)(6)\\3x+y=4\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-3x+6y=-18\\3x+y=4\end{array}\right}\\.\qquad\qquad7y=-14\\.\qquad\qquad y=-2$

Eliminate the y:

$\left\{\begin{array}{ccc}x-2y=6\\3x+y=4\end{array}\right\\\\\text{Multiply by 2}\\\\\left\{\begin{array}{ccc}x-2y=6\\2(3x+y)=(2)(4)\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x-2y=6\\6x+2y=8\end{array}\right}\\\\.\qquad7x=14\\.\qquad x=2$