How do solve the following linear system?: # x-2y = -3 , 2x - 5y=3 #?

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Answer 1 · 2017-03-17T22:36:00

See the entire solution process below:

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

#x - 2y = -3#

#x - 2y + color(red)(2y) = -3 + color(red)(2y)#

#x - 0 = -3 + 2y#

#x = -3 + 2y#

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

#2x - 5y = 3# becomes:

#2(-3 + 2y) - 5y = 3#

#(2 xx -3) + (2 xx 2y) - 5y = 3#

#-6 + 4y - 5y = 3#

#-6 + (4 - 5)y = 3#

#-6 - y = 3#

#color(red)(6) - 6 - y = color(red)(6) + 3#

#0 - y = 9#

#-y = 9#

#color(red)(-1) xx -y = color(red)(-1) xx 9#

#y = -9#

Step 3) Substitute #-9# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = -3 + 2y# becomes:

#x = -3 + (2 xx -9)#

#x = -3 - 18#

#x = -21#

The solution is: #x = -21# and #y = -9# or #(-21, -9)#