how do you solve x + y + z =3 13x + 2z =2 -x -5z =-5?

Answer 1

(1) x + y + z = 3
(2) 13x + 2z = 2
(3) -x - 5z = -5

First, multiply each side of Eqn. 3 by 13, and add the result to Eqn. 2......

13x + 2z = 2
-13x - 65z = -65
----------------------
-63z = -63 ----------------> z = 1


Now that we have the value of z, we can use either Eqn. 2 or Eqn. 3 to find x......we'll use Eqn. 3 for the heck of it:

x = 5 - 5z = 5 - 5(1) = 0

Finally, rearrange Eqn. 1 for y and solve:

y = 3 - x - z = 3 - (0) - (1) = 2


x = 0
y = 2
z = 1