How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #x – 2y = 8# and #x + y = –1#?

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Answer 1 · 2017-07-06T14:26:39

See a solution process below:

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

#x - 2y = 8#

#x - 2y + color(red)(2y) = 8 + color(red)(2y)#

#x - 0 = 8 + 2y#

#x = 8 + 2y#

Step 2) Substitute #(8 + 2y)# for #x# in the second equation and solve for #y#:

#x + y = -1# becomes:

#(8 + 2y) + y = -1#

#8 + 2y + 1y = -1#

#8 + (2 + 1)y = -1#

#8 + 3y = -1#

#-color(red)(8) + 8 + 3y = -color(red)(8) - 1#

#0 + 3y = -9#

#3y = -9#

#(3y)/color(red)(3) = -9/color(red)(3)#

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

#y = -3#

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

#x = 8 + 2y# becomes:

#x = 8 + (2 * -3)#

#x = 8 + (-6)#

#x = 2#

The solution is: #x = 2# and #y = -3# or #(2, -3)#

Because there is at least one point in common these equations are consistent.