How do you solve the system #X+y=10# and #5x-y=8#?

1 Answer

Answer:

See the entire solution process below:

Explanation:

Step 1) Solve the first equation for #x#:

#x + y = 10#

#x + y - color(red)(y) = 10 - color(red)(y)#

#x + 0 = 10 - y#

#x = 10 - y#

Step 2) Substitute #10 - y# for #x# in the second equation and solve for #y#:

#5x - y = 8# becomes:

#5(10 - y) - y = 8#

#(5 xx 10) - (5 xx y) - y = 8#

#50 - 5y - y = 8#

#50 - 6y = 8#

#-color(red)(50) + 50 - 6y = -color(red)(50) + 8#

#0 - 6y = -42#

#-6y = -42#

#(-6y)/color(red)(-6) = -42/color(red)(-6)#

#(color(red)(cancel(color(black)(-6)))y)/cancel(color(red)(-6)) = 7#

#y = 7#

Step 3) Substitute #-7# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = 10 - y# becomes:

#x = 10 - 7#

#x = 10 - 7#

#x = 3#

The solution is: #x = 3# and #y = 7# or #(3, 7)#