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

User Anouar Mokhtari
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1 Answer

27 votes
27 votes

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)

User Ernesto Alfonso
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2.9k points