How do you solve the following system?: #4x -12y =-3 , -3x +y = 18#

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Answer 1 · 2017-01-15T15:02:32

See entire solution process below:

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

#-3x + y = 18#

#-3x + color(red)(3x) + y = 18 + color(red)(3x)#

#0 + y = 18 + 3x#

#y = 3x + 18#

Step 2) Substitute #3x + 18# for #y# in the first equation and solve for #x#:

#4x - 12y = -3#

#4x - 12(3x + 18) = -3#

#4x - 36x - 216 = -3#

#-32x - 216 = -3#

#-32x - 216 + color(red)(216) = -3+ color(red)(216)#

#-32x - 0 = 213#

#-32x = 213#

#(-32x)/color(red)(-32) = 213/color(red)(-32)#

#(color(red)(cancel(color(black)(-32)))x)/cancel(color(red)(-32)) = -6.65625#

#x = -6.65625#

Step 3) Substitute #-6.65625# for #x# into the solution for #y# in the second equation in Step 1 and calculate #y#:

#y = 3x + 18#

#y = (3 xx -6.65625) + 18#

#y = -19.96875 + 18#

#y = -1.96875#

The solution is: #x = -6.65625# and #y = -1.96875#