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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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1 answer

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:

\[ y = 5 \]