Solve the system of equations.

Question

3x+y=2
7x−4y=30(1 point)
Responses

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

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

Answer 1

To solve the system of equations:

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

We will solve the first equation for \( y \) and then substitute that into the second equation.

From the first equation:

\[ y = 2 - 3x \]

Now, substitute \( y \) in the second equation:

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

Distributing the \(-4\):

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

Combine like terms:

\[ 19x - 8 = 30 \]

Now, solve for \( x \):

\[ 19x = 30 + 8 \] \[ 19x = 38 \] \[ x = 2 \]

Now that we have \( x \), substitute it back into the equation for \( y \):

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

Thus, the solution to the system of equations is:

\((2, -4)\)

So the answer is:

(2, −4)