Question

A system of equations is given below.

{x + 3y = 15
{3x + 2y = 10

What is the value of y for the solution to the system? Type your response in the box below.

y =
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Answer 1

To solve the system of equations:

1. \( x + 3y = 15 \) \quad (Equation 1)
2. \( 3x + 2y = 10 \) \quad (Equation 2)

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

From Equation 1, isolate \( x \):

\[
x = 15 - 3y
\]

Now, substitute this expression for \( x \) into Equation 2:

\[
3(15 - 3y) + 2y = 10
\]

Distribute the 3:

\[
45 - 9y + 2y = 10
\]

Combine the terms with \( y \):

\[
45 - 7y = 10
\]

Now, isolate \( y \):

\[
-7y = 10 - 45
\]
\[
-7y = -35
\]
\[
y = \frac{-35}{-7}
\]
\[
y = 5
\]

Thus, the value of \( y \) for the solution to the system is:

\[
y = 5
\]