solve the system of equations

Question

3x+y=2
7x-4y=30

Answer 1

To solve the system of equations:

1) Start by multiplying the first equation by (-4) to eliminate the y variable:

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

2) Next, set up the second equation and the result of step 1 to create a new system of equations:

-12x - 4y = -8
7x - 4y = 30

3) Subtract equation 1 from equation 2:

(7x - 4y) - (-12x - 4y) = 30 - (-8)
7x + 12x - 4y + 4y = 30 + 8
19x = 38

4) Divide both sides of the equation by 19:

x = 38/19
x = 2

5) Substitute the x value of 2 into either of the original equations:

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

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