How do you solve the following system?: #2x -9y =5, x -2y = -5#

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Answer 1 · 2017-05-25T01:21:49

See a solution process below:

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

#x - 2y = -5#

#x - 2y + color(red)(2y) = -5 + color(red)(2y)#

#x - 0 = -5 + 2y#

#x = -5 + 2y#

Step 2) Substitute #(-5 + 2y)# for #x# in the first equation and solve for #y#:

#2x - 9y = 5# becomes:

#2(-5 + 2y) - 9y = 5#

#(2 * -5) + (2 * 2y) - 9y = 5#

#-10 + 4y - 9y = 5#

#-10 + (4 - 9)y = 5#

#-10 + (-5)y = 5#

#-10 - 5y = 5#

#color(red)(10) - 10 - 5y = color(red)(10) + 5#

#0 - 5y = 15#

#-5y = 15#

#(-5y)/color(red)(-5) = 15/color(red)(-5)#

#(color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5)) = -3#

#y = -3#

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

#x = -5 + 2y# becomes:

#x = -5 + (2 * -3)#

#x = -5 + (-6)#

#x = -11#

The solution is: #x = -11# and #y = -3# or #(-11, -3)#