Step 1) Solve the first equation for xx:
x + 2y = 5x+2y=5
x + 2y - color(red)(2y) = 5 - color(red)(2y)x+2y−2y=5−2y
x + 0 = 5 - 2yx+0=5−2y
x = 5 - 2yx=5−2y
Step 2) Substitute (5 - 2y)(5−2y) for xx in the second equation and solve for yy:
-4x + y = -3−4x+y=−3 becomes:
-4(5 - 2y) + y = -3−4(5−2y)+y=−3
(-4 xx 5) - (-4 xx 2y) + y = -3(−4×5)−(−4×2y)+y=−3
-20 - (-8y) + y = -3−20−(−8y)+y=−3
-20 + 8y + y = -3−20+8y+y=−3
-20 + 8y + 1y = -3−20+8y+1y=−3
-20 + (8 + 1)y = -3−20+(8+1)y=−3
-20 + 9y = -3−20+9y=−3
-20 + color(red)(20) + 9y = -3 + color(red)(20)−20+20+9y=−3+20
0 + 9y = 170+9y=17
9y = 179y=17
(9y)/color(red)(9) = 17/color(red)(9)9y9=179
(color(red)(cancel(color(black)(9)))y)/cancel(color(red)(9)) = 17/9
y = 17/9
Step 3) Substitute 17/9 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = 5 - 2y becomes:
x = 5 - (2 xx 17/9)
x = 5 - 34/9
x = (9/9 xx 5) - 34/9
x = 45/9 - 34/9
x = (45 - 34)/9
x = 11/9
The Solution Is:
x = 11/9 and y = 17/9
Or
(11/9, 17/9)
