Step 1) Solve the first equation for yy:
-6x + 6y = -12−6x+6y=−12
(-6x + 6y)/color(red)(6) = -12/color(red)(6)−6x+6y6=−126
(-6x)/color(red)(6) + (6y)/color(red)(6) = -2−6x6+6y6=−2
-x + y = -2−x+y=−2
color(red)(x) - x + y = color(red)(x) - 2x−x+y=x−2
0 + y = x - 20+y=x−2
y = x - 2y=x−2
Step 2) Substitute x - 2x−2 for yy in the second equation and solve for xx:
-10x + 9y = -17−10x+9y=−17 becomes:
-10x + 9(x - 2) = -17−10x+9(x−2)=−17
-10x + (9 * x) - (9 * 2) = -17−10x+(9⋅x)−(9⋅2)=−17
-10x + 9x - 18 = -17−10x+9x−18=−17
-x - 18 = -17−x−18=−17
-x - 18 + color(red)(18) = -17 + color(red)(18)−x−18+18=−17+18
-x - 0 = 1−x−0=1
-x = 1−x=1
color(red)(-1) * -x = color(red)(-1) * 1−1⋅−x=−1⋅1
x = -1x=−1
Step 3) Substitute -1−1 for xx in the solution to the first equation at the end of Step 1 and calculate yy:
y = x - 2y=x−2 becomes:
y = -1 - 2y=−1−2
y = -3y=−3
The solution is: x = -1x=−1 and y = -3y=−3 or (-1, -3)(−1,−3)
