Step 1) Solve the second equation for #y#:
#5x - y = 3#
#-color(red)(3) + 5x - y + color(blue)(y) = -color(red)(3) + 3 + color(blue)(y)#
#-3 + 5x - 0 = 0 + color(blue)(y)#
#-3 + 5x = y#
#y = -3 + 5x#
Step 2) Substitute #(-3 + 5x)# for #y# in the first equation and solve for #x#:
#-9y + 2x = 2# becomes:
#-9(-3 + 5x) + 2x = 2#
#(-9 xx -3) + (-9 xx 5x) + 2x = 2#
#27 - 45x + 2x = 2#
#27 + (-45 + 2)x = 2#
#27 - 43x = 2#
#-color(red)(27) + 27 - 43x = -color(red)(27) + 2#
#0 - 43x = -25#
#-43x = -25#
#(-43x)/color(red)(-43) = (-25)/color(red)(-43)#
#(color(red)(cancel(color(black)(-43)))x)/cancel(color(red)(-43)) = 25/43#
#x = 25/43#
Step 3) Substitute #25/43# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = -3 + 5x# becomes:
#y = -3 + (5 xx 25/43)#
#y = -3 + 125/43#
#y = (-3 xx 43/43) + 125/43#
#y = -129/43 + 125/43#
#y = -4/43#
The solution is: #x = 25/43# and #y = -4/43# or #(25/43, -4/43)#
