Step 1) Solve the first equation for x:
1/2x - 2y = 4
color(red)(2)(1/2x - 2y) = color(red)(2) * 4
(color(red)(2) * 1/2x) - (color(red)(2) * 2y) = 8
color(red)(2)/2x - 4y = 8
1x - 4y = 8
x - 4y + color(red)(4y) = 8 + color(red)(4y)
x - 0 = 8 + 4y
x = 8 + 4y
Step 2) Substitute (8 + 4y) for x in the second equation and solve for y:
4x + y = 2 becomes:
4(8 + 4y) + y = 2
(4 * 8) + (4 * 4y) + y = 2
32 + 16y + y = 2
32 + 16y + 1y = 2
32 + (16 + 1)y = 2
32 + 17y = 2
32 - color(red)(32) + 17y = 2 - color(red)(32)
0 + 17y = -30
17y = -30
(17y)/color(red)(17) = -30/color(red)(17)
(color(red)(cancel(color(black)(17)))y)/cancel(color(red)(17)) = -30/17
y = -30/17
Step 3) Substitute -30/17 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = 8 + 4y becomes:
x = 8 + (4 * -30/17)
x = 8 + (-120/17)
x = 8 - 120/17
x = (17/17 * 8) - 120/17
x = 136/17 - 120/17
x = 16/17
The Solution Is:
x = 16/17 and y = -30/17
Or
(16/17, -30/17)
