Solve the system of equations.

Question

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, −4)
left parenthesis 2 comma negative 4 right parenthesis

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

(−2, 8)

Answer 1

To solve the system of equations:

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

We can use substitution or elimination. Let's use substitution by solving Equation 1 for \( y \):

From Equation 1:

\[ y = 2 - 3x \]

Now substitute \( y \) into Equation 2:

\[ 7x - 4(2 - 3x) = 30 \] \[ 7x - 8 + 12x = 30 \] \[ 19x - 8 = 30 \] \[ 19x = 38 \] \[ x = 2 \]

Now substitute \( x = 2 \) back into Equation 1 to find \( y \):

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

So the solution to the system of equations is:

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

Thus, the answer is:

\((2, -4)\)