Question

8. Solve the system and write the answer as an ordered triple:x + y - z = 42x + 3y - z = 8x - y = -z

Answer 1

Step-by-step explanation

First, isolate x for x+y-z=4:

`x=4-y+z`
`\mathrm{Substitute\:}x=4-y+z`
`\begin{bmatrix}2\left(4-y+z\right)+3y-z=8\\ 4-y+z-y=-z\end{bmatrix}`

Simplifying the equations by applying the distributive property and adding like terms:

`\begin{bmatrix}y+z+8=8\\ -2y+z+4=-z\end{bmatrix}`

Isolate y for y+z+8=8

`y=-z`
`\mathrm{Substitute\:}y=-z`
`\begin{bmatrix}-2\left(-z\right)+z+4=-z\end{bmatrix}`

Simplify:

`\begin{bmatrix}3z+4=-z\end{bmatrix}`
`z=-1`
`\mathrm{For\:}y=-z`
`\mathrm{Substitute\:}z=-1`
`y=-\left(-1\right)`
`\mathrm{Simplify}`
`y=1`
`\mathrm{For\:}x=4-y+z`
`\mathrm{Substitute\:}z=-1,\:y=1`
`x=4-1-1`
`\mathrm{Simplify}`
`x=2`
`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`
`x=2,\:z=-1,\:y=1`

Expressing as an ordered triple:

`(2,1,-1)`