Question

Solve the system of two linear equations.
−3x−4y=−23

3x−5y=5
(1 point)
Responses

(5, 2)
left parenthesis 5 comma 2 right parenthesis

(5,−2)
left parenthesis 5 comma negative 2 right parenthesis

(−5, 2)
left parenthesis negative 5 comma 2 right parenthesis

(−5,−2)

Answer 1

To solve the system of equations:

\[
-3x - 4y = -23 \quad \text{(1)}
\]
\[
3x - 5y = 5 \quad \text{(2)}
\]

We'll use the method of substitution or elimination. Here, I'll use the elimination method.

First, let's multiply equation (2) by 1 to keep it as it is:

\[
3x - 5y = 5 \quad \text{(2)}
\]

Now, we can add equations (1) and (2) by eliminating \(x\). However, it's better to multiply equation (1) by -1 so we can eliminate \(x\):

1. From equation (1):
\[
3x + 4y = 23 \quad \text{(3)}
\]

Now we have:
\[
3x + 4y = 23 \quad \text{(3)}
\]
\[
3x - 5y = 5 \quad \text{(2)}
\]

Now subtract equation (2) from equation (3):

\[
(3x + 4y) - (3x - 5y) = 23 - 5
\]

This simplifies to:

\[
4y + 5y = 18
\]
\[
9y = 18
\]

Now solve for \(y\):

\[
y = \frac{18}{9} = 2
\]

Next, substitute \(y = 2\) back into one of the original equations to find \(x\). We'll use equation (2):

\[
3x - 5(2) = 5
\]
\[
3x - 10 = 5
\]
\[
3x = 15
\]
\[
x = 5
\]

So the solution to the system of equations is:

\[
(x, y) = (5, 2)
\]

The answer is \((5, 2)\).