Step 1) Solve the first equation for yy:
-x + y = 3−x+y=3
-x + color(red)(x) + y = 3 + color(red)(x)−x+x+y=3+x
0 + y = 3 + x0+y=3+x
y = 3 + xy=3+x
Step 2) Substitute (3 + x)(3+x) for yy in the second equation and solve for xx:
5x - 2y = 115x−2y=11 becomes:
5x - 2(3 + x) = 115x−2(3+x)=11
5x - (2 * 3) - (2 * x) = 115x−(2⋅3)−(2⋅x)=11
5x - 6 - 2x = 115x−6−2x=11
5x - 6 + color(red)(6) - 2x = 11 + color(red)(6)5x−6+6−2x=11+6
5x - 0 - 2x = 175x−0−2x=17
5x - 2x = 175x−2x=17
(5 - 2)x = 17(5−2)x=17
3x = 173x=17
(3x)/color(red)(3) = 17/color(red)(3)3x3=173
(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 17/3
x = 17/3
Step 3) Substitute 17/3 for x in the solution to the first equation at the end of Step 1 and calculate y:
y = 3 + x becomes:
y = 3 + 17/3
y = (3/3 * 3) + 17/3
y = 9/3 + 17/3
y = 26/3
The Solution Is:
x = 17/3 and y = 26/3
Or
(17/3, 26/3)
