Question

Solve the following system of linear equations using elimination. 4x-5y=-2 2x+5y=14

Answer 1

$\begin{gathered} 4x-5y=-2 \\ 2x+5y=14 \\ \end{gathered}$

Add both equations to eliminate y

$\begin{gathered} 4x+2x\text{ -5y + 5y =-2+14} \\ 6x=12 \\ x=\frac{12}{6} \\ x=2 \end{gathered}$

substitute x = 2 into the first equation

$\begin{gathered} 4x-5y=-2 \\ 4(2)-5y=-2 \\ 8-5y=-2 \\ -5y=-2-8 \\ -5y=-10 \\ y=\frac{-10}{-5} \\ y=2 \end{gathered}$

Answer is x=2, y=2