# Thread: Systems in 3 variables #2

1. ## Systems in 3 variables #2

Have to find x,y,and z.

1.)
x - y - 5z = -2
y + 3z = 9
x + y + z = 16

HELP ASAP please& thank you

2. Hello, kelsikels!

1) Solve: . $\begin{array}{ccc}
x - y - 5z &=& \text{-}2 \\ \qquad y + 3z &=& 9 \\ x + y + z &=& 16 \end{array}$
There is an infinite number of solutions:

. . $\begin{Bmatrix}x &=& 7 + 2t \\ y &=& 9 - 3t \\ z &=& t \end{Bmatrix}$

3. kelsikels, you should have at least tried yourself! For example, if you add the first and second equations, the "y" and "-y" cancel leaving you an equation in only x and z. If you add the first and third equations, again "y" and "-y", giving a second equation in only x and y. If those are "independent" (neither equation is just a multiple of the other) you can solve those two equations for x and z, then go back and solve for y. If they are not, as Soroban implies, you can solve for, say, x, in terms of z and then solve for y in terms of z. That gives a different solution for each value of z.