Question

Solve the system of equations. 3x+y=2 7x−4y=30 (1 point) Responses (12, 12) left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis (−2, 8) left parenthesis negative 2 comma 8 right parenthesis (2, −2) left parenthesis 2 comma negative 2 right parenthesis (2, −4)

Answer 1

To solve the system of equations:

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

First, we can solve Equation 1 for \( y \):

\[ y = 2 - 3x \]

Now, we substitute this expression for \( y \) into Equation 2:

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

Expanding the left side:

\[ 7x - 8 + 12x = 30 \]

Combine like terms:

\[ 19x - 8 = 30 \]

Add 8 to both sides:

\[ 19x = 38 \]

Now, divide by 19:

\[ x = 2 \]

Next, we 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:

\[ (x, y) = (2, -4) \]

The correct answer is \( (2, -4) \).