Step 1) Solve the second equation for #y#:
#2x + y = 1.5#
#-color(red)(2x) + 2x + y = -color(red)(2x) + 1.5#
#0 + y = -2x + 1.5#
#y = -2x + 1.5#
Step 2) Substitute #(-2x + 1.5)# for #y# in the first equation and solve for #x#:
#-1.5x + 2.5y = 0.5# becomes:
#-1.5x + 2.5(-2x + 1.5) = 0.5#
#-1.5x + (2.5 xx -2x) + (2.5 xx 1.5) = 0.5#
#-1.5x - 5x + 3.75 = 0.5#
#(-1.5 - 5)x + 3.75 = 0.5#
#-6.5x + 3.75 = 0.5#
#-6.5x + 3.75 - color(red)(3.75) = 0.5 - color(red)(3.75)#
#-6.5x + 0 = -3.25#
#-6.5x = -3.25#
#(-6.5x)/color(red)(-6.5) = (-3.25)/color(red)(-6.5)#
#(color(red)(cancel(color(black)(-6.5)))x)/cancel(color(red)(-6.5)) = 0.5#
#x = 0.5#
Step 3) Substitute #0.5# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = -2x + 1.5# becomes:
#y = (-2 xx 0.5) + 1.5#
#y = -1 + 1.5#
#y = 0.5#
The solution is: #x = 0.5# and #y = 0.5# or #(0.5, 0.5)#
