How do you solve the system of equations #10x = - 2y + 1# and #0= 5x + y - 9#?

1 Answer
Jan 16, 2018

See a solution process below:

Explanation:

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

#0 - color(red)(5x) + color(blue)(9) = 5x - color(red)(5x) + y - 9 + color(blue)(9)#

#-5x + 9 = 0 + y - 0#

#-5x + 9 = y#

#y = -5x + 9#

Step 2) Substitute #(-5x + 9)# for #y# in the first equation and solve for #x#:

#10x = -2y + 1# becomes:

#10x = -2(-5x + 9) + 1#

#10x = (-2 xx -5x) + (-2 xx 9) + 1#

#10x = 10x + (-18) + 1#

#10x = 10x - 18 + 1#

#10x = 10x - 17#

#10x - color(red)(10x) = 10x - color(red)(10x) - 17#

#0 = 0 - 17#

#0 != -17#

Because we know #0# does not equal #-17# it means there is no solution to this problem.

Or, the solution is the empty or null set: #x = {O/}#

This also indicates the two lines represented by the equation in the problem are parallel lines and not the same lines.