Solve the system of equations.

Question

3x+y=2

7x−4y=30
(1 point)
Responses

(1/2, 1/2)
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)
left parenthesis negative 2 comma 8 right parenthesis

(2, −4)

Answer 1

To solve the system of equations:

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

We can solve this system using substitution or elimination. Here, we'll use substitution.

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

\[ y = 2 - 3x \]

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

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

Distributing \( -4 \):

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

Combine like terms:

\[ 19x - 8 = 30 \]

Add 8 to both sides:

\[ 19x = 38 \]

Now divide by 19:

\[ x = 2 \]

Now 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:

\(\left(2, -4\right)\)