Question

Solve the system of equations. 3x+y=2 7x−4y=30 (1 point)

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

(2, −2)

Answer 1

To solve the system of equations:

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

We can use the substitution or elimination method. Let's use substitution.

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

\[
y = 2 - 3x
\]

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

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

Distributing the \(-4\):

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

Combining like terms:

\[
19x - 8 = 30
\]

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 answer is:

**(2, -4)**