Question

Question
Solve the system of equations.
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)
left parenthesis 2 comma negative 4 right parenthesis

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 for this case.

From Equation 1, solve for \(y\):

\[
y = 2 - 3x
\]

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

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

Distributing the -4:

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

Combining like terms:

\[
19x - 8 = 30
\]

Add 8 to both sides:

\[
19x = 38
\]

Now divide by 19:

\[
x = 2
\]

Now substitute \(x = 2\) back into the equation for \(y\):

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

The solution to the system of equations is \( (2, -4) \).

Thus, the final answer is:

\[
\boxed{(2, -4)}
\]