Question

1. 4x + 2y = -16 -2x + 3y = -4

Explanation:

Step1: Multiply the second - equation by 2

Multiply $-2x + 3y=-4$ by 2 to get $-4x+6y = - 8$.

Step2: Add the new - equation to the first equation

$(4x + 2y)+(-4x + 6y)=-16+( - 8)$.
Simplify the left - hand side: $4x-4x+2y + 6y=8y$, and the right - hand side: $-16-8=-24$. So, $8y=-24$.

Step3: Solve for y

Divide both sides of $8y=-24$ by 8: $y=\frac{-24}{8}=-3$.

Step4: Substitute y into the second equation

Substitute $y = - 3$ into $-2x+3y=-4$. We get $-2x+3\times(-3)=-4$.
Which simplifies to $-2x-9=-4$.

Step5: Solve for x

Add 9 to both sides: $-2x=-4 + 9=5$.
Then divide both sides by $-2$: $x=-\frac{5}{2}$.

Answer:

$x =-\frac{5}{2},y=-3$