Solve the system of equations.

Question

3x+y=2

7x−4y=30
(1 point)
Responses

(2, −4)
left parenthesis 2 comma negative 4 right parenthesis

(12, 12)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis

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

(−2, 8)

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 use substitution with Equation 1.

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

\[y = 2 - 3x\]

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

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

Now distribute the \(-4\):

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

Combine like terms:

\[19x - 8 = 30\]

Add 8 to both sides:

\[19x = 38\]

Now, divide by 19:

\[x = 2\]

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

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

\[y = 2 - 6\]

\[y = -4\]

Thus, the solution to the system of equations is:

\((2, -4)\)

Therefore, the correct response is:

\((2, -4)\)