Solve the system of equations.

Question

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)

Answer 1

(2, -4)

Answer 2

show how to solve

Answer 3

To solve this system of equations, we can use the substitution method or the elimination method. Here, we will use the substitution method.

Given equations:
1. 3x + y = 2
2. 7x - 4y = 30

From Equation 1, we can solve for y in terms of x:
y = 2 - 3x

Now, substitute this expression for y into Equation 2:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2

Now that we have found x = 2, we can substitute this back into Equation 1 to solve for y:
3(2) + y = 2
6 + y = 2
y = -4

Therefore, the solution to the system of equations is x = 2 and y = -4, or (2, -4).