Question

Solve the system of equations.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, 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 substitution or elimination. Let's solve for \( y \) in Equation 1:

From Equation 1:
\[
y = 2 - 3x
\]

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

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

Simplify:
\[
7x - 8 + 12x = 30
\]
\[
19x - 8 = 30
\]
Add \( 8 \) to both sides:
\[
19x = 38
\]
Now divide by \( 19 \):
\[
x = 2
\]

Now substitute \( x = 2 \) back into the expression 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)**.