Step 1) Solve the first equation for #y#:
#2x + y = 3#
#2x - color(red)(2x) + y = 3 - color(red)(2x)#
#0 + y = 3 - 2x#
#y = 3 - 2x#
Step 2) Substitute #(3 - 2x)# for #y# in the second equation and solve for #x#:
#x - 3y = 5# becomes:
#x - 3(3 - 2x) = 5#
#x - (3 * 3) + (3 * 2x) = 5#
#x - 9 + 6x = 5#
#1x + 6x - 9 = 5#
#(1 + 6)x - 9 = 5#
#7x - 9 = 5#
#7x - 9 + color(red)(9) = 5 + color(red)(9)#
#7x - 0 = 14#
#7x = 14#
#(7x)/color(red)(7) = 14/color(red)(7)#
#(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 2#
#x = 2#
Step 3) Substitute #2# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = 3 - 2x# becomes:
#y = 3 - (2 * 2)#
#y = 3 - 4#
#y = -1#
The Solution Is:
#x = 2# and #y = -1#
Or
#(2, -1)#
