Step 1) Solve the first equation for #y#:
#4x - 2y = 2#
#4x - color(red)(4x) - 2y = 2 - color(red)(4x)#
#0 - 2y = 2 - 4x#
#-2y = 2 - 4x#
#(-2y)/color(red)(-2) = (2 - 4x)/color(red)(-2)#
#(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = 2/color(red)(-2) - (4x)/color(red)(-2)#
#y = -1 + 2x#
Step 2) Substitute #-1 + 2x# for #y# in the second equation and solve for #x#:
#-2x + 5y = -3# becomes:
#-2x + 5(-1 + 2x) = -3#
#-2x + (5 * -1) + (5 * 2x) = -3#
#-2x - 5 + 10x = -3#
#10x - 2x - 5 = -3#
#(10 - 2)x - 5 = -3#
#8x - 5 = -3#
#8x - 5 + color(red)(5) = -3 + color(red)(5)#
#8x - 0 = 2#
#8x = 2#
#(8x)/color(red)(8) = 2/color(red)(8)#
#(color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8)) = 1/4#
#x = 1/4#
Step 3) Subsitute #1/4# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = -1 + 2x# becomes:
#y = -1 + (2 * 1/4)#
#y = -1 + 1/2#
#y = -1/2#
The solution is: #x = 1/4# and #y = -1/2# or #(1/4, -1/2)#
