Question

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

3x−5y=5
(1 point)
Responses

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

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

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

(5,−2)

Answer 1

To solve the system of the two linear equations:

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

We can use either the substitution method or the elimination method. In this case, we will use the elimination method.

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

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

Next, we'll add both equations together to eliminate \(x\):

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

The \(3x\) and \(-3x\) will cancel each other out:

\[
-4y - 5y = -23 + 5
\]

This simplifies to:

\[
-9y = -18
\]

Now, we solve for \(y\):

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

Now that we have \(y = 2\), we can substitute this value back into Equation 2 to find \(x\):

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

This simplifies to:

\[
3x - 10 = 5
\]

Now, we’ll add \(10\) to both sides:

\[
3x = 15
\]

Dividing by \(3\) gives:

\[
x = 5
\]

So the solution to the system of equations is:

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

Therefore, the answer is:

\((5, 2)\)