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)#
