Problem

Solve the following system of equations.
\[
\left\{\begin{aligned}
y & =-2 x+3 \\
-7 x-5 y & =-9
\end{aligned}\right.
\]
Give your answer as an ordered pair $(a, b)$.
Provide your answer below:

Answer

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Answer

The solution to the system of equations is \(\boxed{(2, -1)}\).

Steps

Step 1 :The system of equations is in the form of a linear system. We can solve it by substitution or elimination. Since the first equation is already solved for y, it would be easiest to use substitution.

Step 2 :We can substitute \(y = -2x + 3\) into the second equation and solve for x.

Step 3 :Doing this gives us the equation \(3x - 15 = -9\).

Step 4 :Solving this equation gives us \(x = 2\).

Step 5 :Once we have the value of x, we can substitute it back into the first equation to find the value of y.

Step 6 :Substituting \(x = 2\) into the first equation gives us \(y = -1\).

Step 7 :The solution to the system of equations is \(\boxed{(2, -1)}\).

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