Question

What is the x and the y and the z

Answer 1

`x=2,\: z=3,\: y=-1`

1) Let's solve this system. We can start by rewriting it this way:

`\mleft\{\begin{matrix}3x-8y+z=17 \\ -x+y-z=-6 \\ x-3y=5\end{matrix}\mright.`

Let's pick the 3rd equation and isolate x, from it:

`x=5+3y`

2) Now, we can plug that into the first and the 2nd equation.

Now let's solve this system to find y

`\begin{gathered} \mleft\{\begin{bmatrix}3\mleft(5+3y\mright)-8y+z=17 \\ -\mleft(5+3y\mright)+y-z=-6\end{bmatrix}\mright? \\ 15+y+z=17 \\ -5-2y-z=-6 \\ ------------- \\ y=-z+2 \\ -5-2(-z+2)-z=-6 \\ -5+2z-4-z=-6 \\ z-9=-6 \\ z=9-6 \\ z=3 \end{gathered}`

Now, let's find y based on y=-z+2 plug into that z=3

`\begin{gathered} y=-3+2 \\ y=-1 \end{gathered}`

2.2) And finally, let's find x

`\begin{gathered} x=5+3y \\ x=5+3(-1) \\ x=5-3 \\ x=2 \end{gathered}`

Hence, the answer is:

`x=2,\: z=3,\: y=-1`