Step 1) Solve the second equation for #y#:
#-13x + y = 8#
#color(red)(13x) - 13x + y = color(red)(13x) + 8#
#0 + y = 13x + 8#
#y = 13x + 8#
Step 2) Substitute #(13x + 8)# for #y# in the first equation and solve for #x#:
#5x - 7y = -43# becomes:
#5x - 7(13x + 8) = -43#
#5x - (7 * 13x) - (7 * 8) = -43#
#5x - 91x - 56 = -43#
#(5 - 91)x - 56 = -43#
#-86x - 56 = -43#
#-86x - 56 + color(red)(56) = -43 + color(red)(56)#
#-86x - 0 = 13#
#-86x = 13#
#(-86x)/color(red)(-86) = 13/color(red)(-86)#
#(color(red)(cancel(color(black)(-86)))x)/cancel(color(red)(-86)) = -13/86#
#x = -13/86#
Step 3) Substitute #-13/86# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#;
#y = 13x + 8# becomes:
#y = (13 * -13/86) + 8#
#y = -169/86 + 8#
#y = -169/86 + (86/86 xx 8)#
#y = -169/86 + 688/86#
#y = 519/86#
The solution is: #x = -13/86# and #y = 519/86# or #(-13/86, 519/86)#
