A system of equations is given below.

Question

{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

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. Let's solve it using the substitution method by expressing \( x \) from Equation 1.

From Equation 1:

\[ x = 15 - 3y \]

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

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

Expanding this gives:

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

Combining like terms:

\[ 45 - 7y = 10 \]

Now, isolate \( y \):

\[ -7y = 10 - 45 \]

\[ -7y = -35 \]

Dividing both sides by -7:

\[ y = 5 \]

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

\[ y = 5 \]