How do you solve this system of equations: 3x - 3y + 5z = 13 , 3x + y - 3z = - 5 and 19x - y - 5z = 0?

1 Answer
Dec 26, 2017

x=1/2
y=-1/2
z=2

Explanation:

3x-3y+5z=13
3x+y-3z=-5 iff y=-3x+3z-5
19x-y-5z=0 iff y=19x-5z
=>
3x-3(-3x+3z-5)+5z=13
3x-3(19x-5z)+5z=13
=>
3x+9x-9z+15+5z=13
3x-57x+15z+5z=13
=>
12x-4z=-2 iff z=3x+1/2
-54x+20z=13
=>
-54x+20(3x+1/2)=13
=>
-54x+60x+10=13
=>
6x=3
=>
x=1/2
=>
z=3(1/2)+1/2=2
=>
y=-3(1/2)+3(2)-5
=>
y=-1/2

Check (with a calculator):
3(1/2)-3(-1/2)+5(2)=13
3(1/2)+(-1/2)-3(2)=-5
19(1/2)-(-1/2)-5(2)=0
Worked! :)