Step 1) Solve the second equation for yy:
-6x + 6y = 18−6x+6y=18
(-6x + 6y)/color(red)(6) = 18/color(red)(6)−6x+6y6=186
(-6x)/color(red)(6) + (6y)/color(red)(6) = 3−6x6+6y6=3
-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 first equation and solve for xx:
-2x + 3y = 15−2x+3y=15 becomes:
-2x + 3(3 + x) = 15−2x+3(3+x)=15
-2x + (3 xx 3) + (3 xx x) = 15−2x+(3×3)+(3×x)=15
-2x + 9 + 3x = 15−2x+9+3x=15
-2x + 9 - color(red)(9) + 3x = 15 - color(red)(9)−2x+9−9+3x=15−9
-2x + 0 + 3x = 6−2x+0+3x=6
-2x + 3x = 6−2x+3x=6
(-2 + 3)x = 6(−2+3)x=6
1x = 61x=6
x = 6x=6
Step 3) Substitute 66 for xx in the solution to the second equation at the end of Step 1 and calculate yy:
y = 3 + xy=3+x becomes:
y = 3 + 6y=3+6
y = 9y=9
The Solution Is:
x = 6x=6 and y = 9y=9
Or
(6, 9)(6,9)
