Step 1) Solve the first equation for xx:
x + 2y = 1x+2y=1
x + 2y - color(red)(2y) = 1 - color(red)(2y)x+2y−2y=1−2y
x + 0 = 1 - 2yx+0=1−2y
x = 1 - 2yx=1−2y
Step 2) Substitute (1 - 2y)(1−2y) for xx in the second equation and solve for yy:
6x + 3y = 116x+3y=11 becomes:
6(1 - 2y) + 3y = 116(1−2y)+3y=11
(6 * 1) - (6 * 2y) + 3y = 11(6⋅1)−(6⋅2y)+3y=11
6 - 12y + 3y = 116−12y+3y=11
6 + (-12 + 3)y = 116+(−12+3)y=11
6 + (-9)y = 116+(−9)y=11
6 - 9y = 116−9y=11
6 - color(red)(6) - 9y = 11 - color(red)(6)6−6−9y=11−6
0 - 9y = 50−9y=5
-9y = 5−9y=5
(-9y)/color(red)(-9) = 5/color(red)(-9)−9y−9=5−9
(color(red)(cancel(color(black)(-9)))y)/cancel(color(red)(-9)) = -5/9
y = -5/9
Step 3) Substitute -5/9 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = 1 - 2y becomes:
x = 1 - (2 * -5/9)
x = 1 - (-10/9)
x = 1 + 10/9
x = 9/9 + 10/9
x = 19/9
The Solution Is:
x = 19/9 and y = -5/9
Or
(19/9, -5/9)
