Step 1) Solve the first equation for y:
-3x + y = -4
color(red)(3x) - 3x + y = color(red)(3x) - 4
0 + y = 3x - 4
y = 3x - 4
Step 2) Substitute (3x - 4) for y in the second equation and solve for x:
6y + 4x = 12 becomes:
6(3x - 4) + 4x = 12
(6 * 3x) - (6 * 4) + 4x = 12
18x - 24 + 4x = 12
18x + 4x - 24 = 12
(18 + 4)x - 24 = 12
22x - 24 = 12
22x - 24 + color(red)(24) = 12 + color(red)(24)
22x - 0 = 36
22x = 36
(22x)/color(red)(22) = 36/color(red)(22)
(color(red)(cancel(color(black)(22)))x)/cancel(color(red)(22)) = (2 xx 18)/color(red)(2 xx 11)
x = (color(red)(cancel(color(black)(2))) xx 18)/color(red)(color(black)(cancel(color(red)(2))) xx 11)
x = 18/11
Step 3) Substitute 18/11 for x in the solution to the first equation at the end of Step 1 and calculate y:
y = 3x - 4 becomes:
y = (3 xx 18/11) - 4
y = 54/11 - 4
y = 54/11 - (11/11 xx 4)
y = 54/11 - 44/11
y = 10/11
The Solution Is: x = 18/11 and y = 10/11 or (18/11, 10/11)
