QUESTION 2 - 1 POINT
Solve the following system of equations.
\[
\left\{\begin{aligned}
5 x-8 y & =37 \\
-3 x-7 y & =25
\end{aligned}\right.
\]

Enter your answer as an ordered pair $(x, y)$.

Provide your answer below:

Step 1 ：To solve the given system of linear equations, we can use either substitution or elimination method. In this case, we will use the elimination method to find the values of \( x \) and \( y \).

Step 2 ：We will multiply the first equation by 3 and the second equation by 5 to make the coefficients of \( x \) in both equations equal with opposite signs, and then add the equations to eliminate \( x \).

Step 3 ：Multiplying the first equation by 3: \( 3(5x - 8y) = 3(37) \) gives \( 15x - 24y = 111 \).

Step 4 ：Multiplying the second equation by 5: \( 5(-3x - 7y) = 5(25) \) gives \( -15x - 35y = 125 \).

Step 5 ：Adding the two new equations \( 15x - 24y + (-15x - 35y) = 111 + 125 \) to eliminate \( x \) gives \( -59y = 236 \).

Step 6 ：Solving for \( y \) gives \( y = -4 \).

Step 7 ：Substitute \( y = -4 \) into the first original equation \( 5x - 8(-4) = 37 \) to find \( x \).

Step 8 ：Solving the equation \( 5x + 32 = 37 \) gives \( x = 1 \).

Step 9 ：The solution to the system of equations is \( x = 1 \) and \( y = -4 \).

Step 10 ：Final Answer: \(\boxed{(1, -4)}\)