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 =
Math Equation Response Question
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Answer 1

To solve the system of equations given by

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

we can use either substitution or elimination. Let's use substitution.

From equation (1), we can express \(x\) in terms of \(y\):

\[
x = 15 - 3y
\]

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

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

Now, distribute the 3:

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

Combine like terms:

\[
45 - 7y = 10
\]

To isolate \(y\), subtract 45 from both sides:

\[
-7y = 10 - 45
\]
\[
-7y = -35
\]

Now, divide by -7:

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

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

\[
\boxed{5}
\]