Step 1) Solve the first equation for yy:
-6x + y = -8−6x+y=−8
-6x + color(red)(6x) + y = -8 + color(red)(6x)−6x+6x+y=−8+6x
0 + y = -8 + 6x0+y=−8+6x
y = -8 + 6xy=−8+6x
Step 2) Substitute (-8 + 6x)(−8+6x) for yy in the second equation and solve for xx
2x + 3y = 42x+3y=4 becomes:
2x + 3(-8 + 6x) = 42x+3(−8+6x)=4
2x + (3 xx -8) + (3 xx 6x) = 42x+(3×−8)+(3×6x)=4
2x - 24 + 18x = 42x−24+18x=4
2x + 18x - 24 = 42x+18x−24=4
(2 + 18)x - 24 = 4(2+18)x−24=4
20x - 24 = 420x−24=4
20x - 24 + color(red)(24) = 4 + color(red)(24)20x−24+24=4+24
20x - 0 = 2820x−0=28
20x = 2820x=28
(20x)/color(red)(20) = 28/color(red)(20)20x20=2820
(color(red)(cancel(color(black)(20)))x)/cancel(color(red)(20)) = 7/5
x = 7/5
Step 3) Substitute 7/5 for x in the solution to the first equation at the end of Step 1 and calculate y:
y = -8 + 6x becomes:
y = -8 + (6 xx 7/5)
y = (5/5 xx -8) + 42/5
y = -40/5 + 42/5
y = 2/5
The Solution Is:
x = 7/5 and y = 2/5
Or
(7/5, 2/5)
