Question

Solve the system of two linear equations.
−3x−4y=−23
3x−5y=5


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

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

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

(−5,−2)

Answer 1

To solve the system of equations:

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

We can use the method of elimination or substitution. Here, let's use the elimination method.

First, we can multiply Equation 2 by 1 (to keep it the same) and rearrange:

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

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

- Adding both equations:

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

This simplifies to:

\[
-4y - 5y = -18
\]
\[
-9y = -18
\]
\[
y = 2
\]

Now that we have the value for \(y\), we can substitute it back into one of the original equations to find \(x\). Let's use Equation 2:

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

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

Thus, the solution to the system of equations is \( (5, 2) \).

Verifying with both equations:

1. For Equation 1:
\(-3(5) - 4(2) = -15 - 8 = -23\) (correct)

2. For Equation 2:
\(3(5) - 5(2) = 15 - 10 = 5\) (correct)

Therefore, the solution is \( \boxed{(5, 2)} \).