Step 1) Solve the first equation for xx:
x + 7y = 3x+7y=3
x + 7y - color(red)(7y) = 3 - color(red)(7y)x+7y−7y=3−7y
x + 0 = 3 - 7yx+0=3−7y
x = 3 - 7yx=3−7y
Step 2) Substitute (3 - 7y)(3−7y) for xx in the second equation and solve for yy:
12x - 9y = 212x−9y=2 becomes:
12(3 - 7y) - 9y = 212(3−7y)−9y=2
(12 xx 3) - (12 xx 7y) - 9y = 2(12×3)−(12×7y)−9y=2
36 - 84y - 9y = 236−84y−9y=2
36 + (-84 - 9)y = 236+(−84−9)y=2
36 + (-93)y = 236+(−93)y=2
36 - 93y = 236−93y=2
36 - color(red)(36) - 93y = 2 - color(red)(36)36−36−93y=2−36
0 - 93y = -340−93y=−34
-93y = -34−93y=−34
(-93y)/color(red)(-93) = -34/color(red)(-93)−93y−93=−34−93
(color(red)(cancel(color(black)(-93)))y)/cancel(color(red)(-93)) = 34/93
y = 34/93
Step 3) Substitute 34/93 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = 3 - 7y becomes:
x = 3 - (7 xx 34/93)
x = (93/93 xx 3) - 238/93
x = 279/93 - 238/93
x = 41/93
The Solution Is:
x = 41/93 and y = 34/93
Or
(41/93, 34/93)
