Use the elimination method to solve the follow system of equations.

Question

9x - 7y = 22

x + 3y = -24

A 3,-9
B 0, -8
C -3, -7
D 4,2

Answer 1

To solve the system of equations using the elimination method, we have:

1. $9x-7y=22$ (Equation 1)
2. $x+3y=-24$ (Equation 2)

First, we will manipulate Equation 2 so that it can be easily eliminated with Equation 1. We can multiply Equation 2 by 9 to match the coefficient of $x$ in Equation 1:

$$9(x+3y)=9(-24)$$

This gives us:

$$9x+27y=-216(Equation3)$$

Now we have a new equation (Equation 3) and will write the system again:

1. $9x-7y=22$ (Equation 1)
2. $9x+27y=-216$ (Equation 3)

Next, we'll subtract Equation 1 from Equation 3 to eliminate $x$:

$$(9x+27y)-(9x-7y)=-216-22$$

This simplifies to:

$$27y+7y=-238$$

$$34y=-238$$

Now, solve for $y$:

$$y=\frac{-238}{34}=-7$$

Next, we substitute $y=-7$ back into Equation 2 to solve for $x$:

$$x+3(-7)=-24$$

$$x-21=-24$$

Adding 21 to both sides gives us:

$$x=-3$$

So, we have $x=-3$ and $y=-7$. The solution is:

$$(x,y)=(-3,-7)$$

Looking at the answer choices:

A) (3, -9)
B) (0, -8)
C) (-3, -7)
D) (4, 2)

The correct answer is C) (-3, -7).