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)#
