Step 1) Solve the second equation for xx:
x - 2y = 6x−2y=6
x - 2y + color(red)(2y) = 6 + color(red)(2y)x−2y+2y=6+2y
x - 0 = 6 + 2yx−0=6+2y
x = 6 + 2yx=6+2y
Step 2) Substitute 6 + 2y6+2y for xx in the first equation and solve for yy:
1/2x + 2y = 1212x+2y=12 becomes:
1/2(6 + 2y) + 2y = 1212(6+2y)+2y=12
(1/2 * 6) + (1/2 * 2y) + 2y = 12(12⋅6)+(12⋅2y)+2y=12
6/2+ (1/color(red)(cancel(color(black)(2))) * color(red)(cancel(color(black)(2)))y) + 2y = 12
3+ 1y + 2y = 12
3+ (1 + 2)y = 12
3+ 3y = 12
-color(red)(3) + 3+ 3y = -color(red)(3) + 12
0+ 3y = 9
3y = 9
(3y)/color(red)(3) = 9/color(red)(3)
(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = 3
y = 3
Step 3) Substitute 3 for y in the solution to the second equation at the end of Step 1 and calculate x:
x = 6 + 2y becomes:
x = 6 + (2 * 3)
x = 6 + 6
x = 12
The solution is: x = 12 and y = 3 or (12, 3)
