How do you solve this system of equations: #-6x + 6y = - 12;- 10x + 9y = - 17#?

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Answer 1 · 2017-04-18T13:33:48

See the entire solution process below:

Step 1) Solve the first equation for #y#:

#-6x + 6y = -12#

#(-6x + 6y)/color(red)(6) = -12/color(red)(6)#

#(-6x)/color(red)(6) + (6y)/color(red)(6) = -2#

#-x + y = -2#

#color(red)(x) - x + y = color(red)(x) - 2#

#0 + y = x - 2#

#y = x - 2#

Step 2) Substitute #x - 2# for #y# in the second equation and solve for #x#:

#-10x + 9y = -17# becomes:

#-10x + 9(x - 2) = -17#

#-10x + (9 * x) - (9 * 2) = -17#

#-10x + 9x - 18 = -17#

#-x - 18 = -17#

#-x - 18 + color(red)(18) = -17 + color(red)(18)#

#-x - 0 = 1#

#-x = 1#

#color(red)(-1) * -x = color(red)(-1) * 1#

#x = -1#

Step 3) Substitute #-1# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:

#y = x - 2# becomes:

#y = -1 - 2#

#y = -3#

The solution is: #x = -1# and #y = -3# or #(-1, -3)#