Solve the system of equations. 3x+y=2 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 (12, 12) left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis (2, −4)

1 answer

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From the first equation, we can solve for y:

3x + y = 2
=> y = 2 - 3x

Now we substitute this value of y into the second equation:

7x - 4(2 - 3x) = 30
=> 7x - 8 + 12x = 30
=> 19x - 8 = 30
=> 19x = 38
=> x = 2

We can substitute this value of x back into the first equation to solve for y:

3(2) + y = 2
=> 6 + y = 2
=> y = -4

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