Step 1) Solve the first equation for y:
2x - y = 4
-color(red)(2x) + 2x - y = -color(red)(2x) + 4
0 - y = -2x + 4
-y = -2x + 4
color(red)(-1) xxx -y = color(red)(-1)(-2x + 4)
y = (color(red)(-1) xx -2x) + (color(red)(-1) xx 4)
y = 2x - 4
Step 2) Substitute (2x - 4) for y in the second equation and solve for x:
7x + 3y = 27 becomes:
7x + 3(2x - 4) = 27
7x + (3 xx 2x) - (3 xx 4) = 27
7x + 6x - 12 = 27
(7 + 6)x - 12 = 27
13x - 12 = 27
13x - 12 + color(red)(12) = 27 + color(red)(12)
13x - 0 = 39
13x = 39
(13x)/color(red)(13) = 39/color(red)(13)
(color(red)(cancel(color(black)(13)))x)/cancel(color(red)(13)) = 3
x = 3
Step 3) Substitute 3 for x in the solution to the first equation at the end of Step 1 and calculate y:
y = 2x - 4 becomes:
y = (2 xx 3) - 4
y = 6 - 4
y = 2
The Solution Is: x = 3 and y = 2 or (3, 2)
