Question

Solving with Elimination Quick Check
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Question
Solve the system of two linear equations.
−3x−4y=−23

3x−5y=5
(1 point)
Responses

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

(5, 2)
left parenthesis 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 using elimination, we have the following two equations:

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

Let's manipulate these equations to eliminate one of the variables. Here, we can add the two equations together since the coefficients of \(x\) in the first equation is \(-3\) and in the second equation is \(3\), which will eliminate \(x\):

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

Adding the two equations:

\[
(-3x + 3x) + (-4y - 5y) = -23 + 5
\]
\[
0x - 9y = -18
\]

This simplifies to:

\[
-9y = -18
\]

To solve for \(y\), divide both sides by \(-9\):

\[
y = 2
\]

Now that we have the value of \(y\), we can substitute it back into one of the original equations to find \(x\). Let's use the second equation:

\[
3x - 5y = 5
\]
Substituting \(y = 2\):

\[
3x - 5(2) = 5
\]
\[
3x - 10 = 5
\]
Now we add \(10\) to both sides:

\[
3x = 15
\]
And divide by \(3\):

\[
x = 5
\]

Thus, the solution to the system of equations is:

\((5, 2)\)

Therefore, the response is:

**(5, 2)**