Given: #10x + 8y = 16 " and " 5y = 4x - 15#
Put both equations in the same form: #Ax + By = C# so that you can solve the system of equations using elimination.
#" "10x + 8y = 16 " and " 4x -5y = 15#
Find #x#:
To eliminate #y#, multiply the first equation by #5# and the second equation by #8#:
#" "50x + 40y = 80#
#ul(+32x - 40y = 120)#
#" "82x " " = 200#; #" "x = 200/82 = 100/41#
Find #y#:
Substitute #x# into either one of the equations and solve for #y#:
#10/1 * 100/41 + 8y = 16#
#1000/41 + 8y = 16#
#8y = 16/1 - 1000/41#
#8y = 656/41 - 1000/41 = -344/41#
#y = (-344/41)/8 = -344/41 * 1/8 = -43/41#
