Step 1) Solve the second equation for #y#:
#2x + y = 3#
#2x + y - color(red)(2x) = 3 - color(red)(2x)#
#2x - color(red)(2x) + y = 3 - 2x#
#0 + y = 3 - 2x#
#y = 3 - 2x#
Step 2) Substitute #3 - 2x# for #y# in the first equation and solve for #x#:
#3x + 2y = 4# becomes:
#3x + 2(3 - 2x) = 4#
#3x + (2 xx 3) - (2 xx 2x) = 4#
#3x + 6 - 4x = 4#
#3x - 4x + 6 = 4#
#(3 - 4)x + 6 = 4#
#-1x + 6 = 4#
#-x + 6 - color(red)(6) = 4 - color(red)(6)#
#-x + 0 = -2#
#-x = -2#
#color(red)(-1) xx -x = color(red)(-1) xx -2#
#x = 2#
Step 3) Substitute #2# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = 3 - 2x# becomes:
#y = 3 - (2 xx 2)#
#y = 3 - 4#
#y = -1#
The solution is #x = 2# and #y = -1# or #(2, -1)#
