Question

Solve the system of equations.
3x+y=2

7x−4y=30
(1 point)
Responses

(−2, 8)

(2, −2)

(2, −4)

(12, 12)

Answer 1

To solve the system of equations:

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

We will start by solving Equation 1 for \( y \):

\[
y = 2 - 3x
\]

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

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

Expanding this gives:

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

Combining like terms:

\[
19x - 8 = 30
\]

Now, add 8 to both sides:

\[
19x = 38
\]

Dividing both sides 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:

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

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