Answer
x = 1, y = -3
Explanation
Given system of equations:
[tex]\begin{gathered} 4x+2y=-2----i \\ -4x-3y=5----ii \end{gathered}[/tex]Using the elimination method, add (i) and (ii) together:
[tex]\begin{gathered} 4x+(-4x)+2y+(-3y)=-2+5 \\ 4x-4x+2y-3y=3 \\ -y=3 \\ \text{Multiply both sides by -1} \\ y=-3 \end{gathered}[/tex]To solve for x, put y = -3 into (i)
[tex]\begin{gathered} \text{Recall (i)} \\ 4x+2y=-2-----i \\ 4x+2(-3)=-2 \\ 4x-6=-2 \\ \text{Add 6 to both sides} \\ 4x-6+6=-2+6 \\ 4x=4 \\ \text{Divide both sides by 4} \\ \frac{4x}{4}=\frac{4}{4} \\ x=1 \end{gathered}[/tex]The solution to the system of equations is x = 1 and y = -3
