Question

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

(2, −4)
left parenthesis 2 comma negative 4 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 the substitution or elimination method. Here, I'll use substitution.

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

\[ y = 2 - 3x \]

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

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

Distributing \(-4\):

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

Combining like terms:

\[ 19x - 8 = 30 \]

Adding 8 to both sides gives:

\[ 19x = 38 \]

Dividing by 19, we find:

\[ x = 2 \]

Now, we substitute \(x = 2\) back into the expression we found for \(y\):

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

So, the solution to the system of equations is:

\[ (x, y) = (2, -4) \]

Thus, the answer is:

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