Solve the system of equations.

Question

3x+y=2
7x−4y=30 (1 point)
Responses

(2, −2)
left parenthesis 2 comma negative 2 right parenthesis

(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis

(12, 12)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis

(2, −4)
left parenthesis 2 comma negative 4 right parenthesis
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Answer 1

To solve the system of equations:

1. \( 3x + y = 2 \) (Equation 1)
2. \( 7x - 4y = 30 \) (Equation 2)

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

From Equation 1: \[ y = 2 - 3x \]

Now, we can substitute \( y \) into Equation 2:

\[ 7x - 4(2 - 3x) = 30 \]

Simplifying this: \[ 7x - 8 + 12x = 30 \] \[ 19x - 8 = 30 \] Adding 8 to both sides: \[ 19x = 38 \] Dividing by 19: \[ x = 2 \]

Now, substitute \( x = 2 \) back into the equation for \( y \): \[ y = 2 - 3(2) = 2 - 6 = -4 \]

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

So the correct answer is: \[ \boxed{(2, -4)} \]