Solve the system of equations.

Question

3x+y=2
7x−4y=30 (1 point)
Responses

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

(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis

(12, 12)
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, we can use the method of elimination by multiplying the first equation by 4 to eliminate y:

4(3x+y) = 4(2)
12x + 4y = 8

Now we have the system of equations:
12x + 4y = 8
7x - 4y = 30

Adding the two equations together, we get:
(12x + 4y) + (7x - 4y) = 8 + 30
19x = 38
x = 2

Substituting x = 2 into the first equation, we get:
3(2) + y = 2
6 + y = 2
y = -4

Therefore, the solution to the system of equations is (2, -4).