Question

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 negative 5 comma 2 right parenthesis

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

(−5,−2)

Answer 1

To solve the system of equations given by:

1. \(-3x - 4y = -23\) (Equation 1)
2. \(3x - 5y = 5\) (Equation 2)

Let's use the method of substitution or elimination. Here, we will use elimination.

First, we can multiply Equation 2 by 1 to make it easier to eliminate \(x\):

\[
3x - 5y = 5
\]

Now we can add Equation 1 and Equation 2 together:

1. \(-3x - 4y = -23\)
2. \(3x - 5y = 5\)

Adding those two equations:

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

This simplifies to:

\[
0x - 9y = -18
\]

Now we can solve for \(y\):

\[
-9y = -18
\]

Dividing both sides by \(-9\):

\[
y = 2
\]

Now that we have \(y\), we'll substitute it back into one of the original equations to find \(x\). We'll use Equation 2:

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

Thus, the solution to the system of equations is:

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

So, the answer is:

\((5, 2)\)