How do you solve the system of equations #3x+2y=9,x-y=2#?

Question

2066 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-27T17:35:14

See the entire solution process below:

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

#x - y = 2#

#x - y + y = 2 + y#

#x - 0 = 2 + y#

#x = 2 + y#

Step 2) Substitute #2 + y# for #x# in the first equation and solve for #y#:

#3(2 + y) + 2y = 9#

#6 + 3y + 2y = 9#

#6 + 5y = 9#

#6 - 6 + 5y 9 - 6#

#0 + 5y = 3#

#5y = 3#

#(5y)/5 = 3/5#

#(color(red)(cancel(color(black)(5)))y)/color(red)(cancel(color(black)(5))) = 3/5#

#y = 3/5#

Step 3) Substitute #3/5# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:

#x = 2 + 3/5#

#x = (5/5 xx 2) + 3/5#

#x = 10/5 + 3/5#

#x = 13/5#

The solution is:

#x = 13/5# and #y = 3/5#