Question

Solve the system of linear equations using the elimination method. Write your answer as a coordinate on the xy
-coordinate plane.

y+3x=−2


2y−3x=14


(1 point)
Responses

(-2, 4)
(-2, 4)

(-6, 16)
(-6, 16)

(4, -2)
(4, -2)

(6, 16)
(6, 16)
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Answer 1

To solve the system of linear equations using the elimination method, we have:

1. \( y + 3x = -2 \) (Equation 1)
2. \( 2y - 3x = 14 \) (Equation 2)

First, let's rewrite the equations in the standard form:

1. \( y = -2 - 3x \) (from Equation 1)
2. \( 2y = 3x + 14 \) (from Equation 2)

Now we can eliminate \( x \) or \( y \). We can eliminate \( y \) by multiplying Equation 1 by 2:

\[ 2(y + 3x) = 2(-2) \]
This gives us:
\[ 2y + 6x = -4 \] (Equation 3)

Now we have:
\[
\begin{align*}
2y + 6x &= -4 \quad \text{(Equation 3)} \\
2y - 3x &= 14 \quad \text{(Equation 2)}
\end{align*}
\]

Next, we can subtract Equation 2 from Equation 3 to eliminate \( 2y \):

\[ (2y + 6x) - (2y - 3x) = -4 - 14 \]

This simplifies to:
\[ 6x + 3x = -18 \]
\[ 9x = -18 \]

Now we can solve for \( x \):
\[ x = \frac{-18}{9} = -2 \]

Next, substitute \( x = -2 \) back into Equation 1 to find \( y \):

\[ y + 3(-2) = -2 \]
\[ y - 6 = -2 \]
\[ y = -2 + 6 \]
\[ y = 4 \]

Thus, the solution to the system of equations is:
\[ (x, y) = (-2, 4) \]

Therefore, the answer is:

**(-2, 4)**