Question

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

3x + 5y = 1

7x + 4y = −13

−3
−1
2
5

Answer 1

To solve the system of equations:

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

We can use the elimination or substitution method. Here, we will use the elimination method for clarity.

First, let's multiply Equation 1 by 7 and Equation 2 by 3 to align the coefficients of \( x \):

\[
7(3x + 5y) = 7(1) \implies 21x + 35y = 7 \quad (Equation 3)
\]

\[
3(7x + 4y) = 3(-13) \implies 21x + 12y = -39 \quad (Equation 4)
\]

Now we have:

**Equation 3:** \( 21x + 35y = 7 \)

**Equation 4:** \( 21x + 12y = -39 \)

Next, we subtract Equation 4 from Equation 3:

\[
(21x + 35y) - (21x + 12y) = 7 - (-39)
\]

This simplifies to:

\[
35y - 12y = 7 + 39
\]

Combining like terms gives:

\[
23y = 46
\]

Now, divide both sides by 23:

\[
y = 2
\]

Thus, the \( y \)-value of the solution to the system of equations is \( \boxed{2} \).