Question

solve by elimination: 7x - 9y = 29; 7x + 2y = -15

Explanation:

Step1: Subtract the two equations

We have the system of equations:

$$\begin{cases} 7x - 9y = 29 \\ 7x + 2y = -15 \end{cases}$$

Subtract the second equation from the first equation:
$$(7x - 9y)-(7x + 2y)=29-(-15)$$
Simplify the left side: $7x - 9y - 7x - 2y=-11y$
Simplify the right side: $29 + 15 = 44$
So we get $-11y = 44$

Step2: Solve for y

Divide both sides of $-11y = 44$ by $-11$:
$$y=\frac{44}{-11}=-4$$

Step3: Substitute y into one of the original equations to solve for x

Substitute $y = - 4$ into the second equation $7x+2y=-15$:
$$7x+2\times(-4)=-15$$
Simplify: $7x-8=-15$
Add 8 to both sides: $7x=-15 + 8=-7$
Divide both sides by 7: $x=\frac{-7}{7}=-1$

Answer:

The solution to the system of equations is $(-1,-4)$, so the correct option is the one with $(-1,-4)$ (the purple box option: $(-1,-4)$)