Question

Solve for the solutions, using substitution method

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

Group of answer choices

(0,-1)

(5,0)

(0,5)

(-1,0)

Answer 1

To solve the system of equations using the substitution method, we will first substitute the expression for \( x \) from the first equation into the second equation.

The equations are:
1. \( x = -3y + 15 \)
2. \( 3x + 2y = 10 \)

Now, we'll substitute \( x \) in the second equation:

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

Now, we'll distribute the 3:

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

Combine like terms:

\[
-9y + 2y + 45 = 10
\]
\[
-7y + 45 = 10
\]

Subtract 45 from both sides:

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

Now, divide by -7:

\[
y = 5
\]

Now that we have \( y \), we can find \( x \) using the first equation:

\[
x = -3(5) + 15
\]
\[
x = -15 + 15
\]
\[
x = 0
\]

Thus, the solution is \( (0, 5) \).

From the given choices, the correct answer is:

\((0, 5)\)