Question

What is the y-value of the solution to the system of equations?

3x + 5y = 1

7x + 4y = −13

−3
−1
2

Answer 1

To solve the system of equations:

1. **3x + 5y = 1** (Equation 1)
2. **7x + 4y = -13** (Equation 2)

We can use the method of substitution or elimination. Here, I will use substitution.

First, let's solve Equation 1 for \(y\):

\[
5y = 1 - 3x
\]
\[
y = \frac{1 - 3x}{5}
\]

Now we substitute this expression for \(y\) into Equation 2:

\[
7x + 4\left(\frac{1 - 3x}{5}\right) = -13
\]

Multiply through by 5 to eliminate the fraction:

\[
35x + 4(1 - 3x) = -65
\]
\[
35x + 4 - 12x = -65
\]
\[
23x + 4 = -65
\]
\[
23x = -65 - 4
\]
\[
23x = -69
\]
\[
x = -3
\]

Now we'll substitute \(x = -3\) back into the equation we derived for \(y\):

\[
y = \frac{1 - 3(-3)}{5}
\]
\[
y = \frac{1 + 9}{5}
\]
\[
y = \frac{10}{5} = 2
\]

Thus, the y-value of the solution to the system of equations is:

\[
\boxed{2}
\]