Step 1) Solve the first equation for yy:
2x - y = 42x−y=4
2x - color(blue)(4) - y + color(red)(y) = 4 - color(blue)(4) + color(red)(y)2x−4−y+y=4−4+y
2x - 4 - 0 = 0 + y2x−4−0=0+y
2x - 4 = y2x−4=y
y = 2x - 4y=2x−4
Step 2) Substitute (2x - 4)(2x−4) for yy in the second equation and solve for xx:
7x + 3y = 277x+3y=27 becomes:
7x + 3(2x - 4) = 277x+3(2x−4)=27
7x + (3 xx 2x) - (3 xx 4) = 277x+(3×2x)−(3×4)=27
7x + 6x - 12 = 277x+6x−12=27
(7 + 6)x - 12 = 27(7+6)x−12=27
13x - 12 = 2713x−12=27
13x - 12 + color(red)(12) = 27 + color(red)(12)13x−12+12=27+12
13x - 0 = 3913x−0=39
13x = 3913x=39
(13x)/color(red)(13) = 39/color(red)(13)13x13=3913
(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)
