Question

A system of equations is given below.



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

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

y =

Answer 1

To solve the system of equations, we have:

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

We can solve these equations using the substitution or elimination method. Here, we will use the substitution method.

First, we will solve Equation 1 for \( x \):

\[
x = 15 - 3y
\]

Now we can substitute \( x \) in Equation 2:

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

Distributing \( 3 \):

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

Combining like terms:

\[
45 - 7y = 10
\]

Next, we will isolate \( y \):

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

Thus, the value of \( y \) is:

\[
\boxed{5}
\]