How do solve the following linear system?: # 9 x-6y =3 , 3x + y = -20 #?

1 Answer
Jun 19, 2018

Answer:

See a solution process below:

Explanation:

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

#3x + y = -20#

#3x - color(red)(3x) + y = -color(red)(3x) - 20#

#0 + y = -3x - 20#

#y = -3x - 20#

Step 2) Substitute #(-3x - 20)# for #y# in the first equation and solve for #x#:

#9x - 6y = 3# becomes:

#9x - 6(-3x - 20) = 3#

#9x - (6 xx -3x) - (6 xx -20) = 3#

#9x - (-18x) - (-120) = 3#

#9x + 18x + 120 = 3#

#(9 + 18)x + 120 = 3#

#27x + 120 = 3#

#27x + 120 - color(red)(120) = 3 - color(red)(120)#

#27x + 0 = -117#

#27x = -117#

#(27x)/color(red)(27) = -117/color(red)(27)#

#(color(red)(cancel(color(black)(27)))x)/cancel(color(red)(27)) = -(9 xx 13)/color(red)(9 xx 3)#

#x = -(color(red)(cancel(color(black)(9))) xx 13)/color(red)(color(black)(cancel(color(red)(9))) xx 3)#

#x = -13/3#

Step 3) Substitute #-13/3# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:

#y = -3x - 20# becomes:

#y = -(3 xx -13/3) - 20#

#y = -(-13) - 20#

#y = 13 - 20#

#y = -7#

The Solution Is:

#x = -13/3# and #y = -7#

Or

#(-13/3, -7)#