3x+y=2

Question

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

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

(2, −4)

Answer 1

To solve the system of equations

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

we can use substitution or elimination. Let's use substitution for clarity.

From the first equation, we can express \(y\) in terms of \(x\):

\[ y = 2 - 3x \]

Now, we substitute this expression for \(y\) into the second equation:

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

Expanding this gives:

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

Combining like terms:

\[ 19x - 8 = 30 \]

Adding 8 to both sides:

\[ 19x = 38 \]

Dividing by 19:

\[ x = 2 \]

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

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

So the solution is:

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

The correct response from your choices is:

(2, −4).