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?

Answer 1

To solve the system of equations:

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

We can use the substitution or elimination method. Here, let's use the substitution method.

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

\[
x = 15 - 3y
\]

Next, we will substitute this expression for \( x \) into Equation 2:

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

Expanding this, we get:

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

Combining like terms:

\[
45 - 7y = 10
\]

Next, isolate \( y \) by subtracting 45 from both sides:

\[
-7y = 10 - 45
\]

This simplifies to:

\[
-7y = -35
\]

Now, divide both sides by -7:

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

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

\[
\boxed{5}
\]