Step 1) Solve the second equation for #y#:
#10x + y = -3#
#-color(red)(10x) + 10x + y = -color(red)(10x) - 3#
#0 + y = -10x - 3#
#y = -10x - 3#
Step 2) Substitute #(-10x - 3)# for #y# in the first equation and solve for #x#:
#-5x - 2y = 9# becomes:
#-5x - 2(-10x - 3) = 9#
#-5x + (-2 xx -10x) + (-2 xx -3) = 9#
#-5x + 20x + 6 = 9#
#(-5 + 20)x + 6 = 9#
#15x + 6 = 9#
#15x + 6 - color(red)(6) = 9 - color(red)(6)#
#15x + 0 = 3#
#15x = 3#
#(15x)/color(red)(15) = 3/color(red)(15)#
#(color(red)(cancel(color(black)(15)))x)/cancel(color(red)(15)) = 3/color(red)(3 xx 5)#
#x = color(red)(cancel(color(black)(3)))/color(red)(color(black)(cancel(color(red)(3))) xx 5)#
#x = 1/5#
Step 3) Substitute #1/5# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = -10x - 3# becomes:
#y = (-10 xx 1/5) - 3#
#y = -2 - 3#
#y = -5#
The solution is: #x = 1/5# and #y = -5# or #(1/5, -5)#
