Question

Solve the following system of linear equations:

16x-16y+24z=120
-13x +13y -20z =-99
51x -51y +77z =384
I know there are infinitely many solutions with 1 arbitrary parameter(which is y=y) Im having trouble with x and z. Help?

Answer 1

treat y like any constant and find x and z like functions of y

Answer 2

still not getting the answer. if i put a 1 in for y, i solve to x=13/2-3/2z and z=13/3-2/3x which is wrong, where am i going wrong?

Answer 3

y = x-3
z = 3

Answer 4

put y = p for example
then rearange equations like this:
16x+24z=120+16p
-13x-20z=-99-13p
51x+77z=384+51p
so now you have 3 equations qith 2 uknown. Choose any 2 of them and solve them to find x and z

Answer 5

ok, I will try that. Thank you for your help!

Answer 6

yw