QUESTION 2 - 1 POINT
Solve the following system of equations.
$$\{\begin{array}{rl}5x-8y& =37\\ -3x-7y& =25\end{array}$$

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: $\boxed{{\displaystyle (1,-4)}}$