Question

Solving Linear Systems With Three Variables. Solve. Please show steps.
{x+5y-2z=15
{3x-7y+4z=-7
{2x+4y-3z=21

Answer 1

\[\left[\begin{matrix}1&5 & -2 \\ 3 &-7 &4\\2 &4&-3 \end{matrix}\right]\left(\begin{matrix} x\\y \\ z\end{matrix}\right)=\left(\begin{matrix} 15\\-7 \\21 \end{matrix}\right)\]

Answer 2

2x+10y-4z=30
2x+4y-3z= 21
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6y -z =9

3x+15y-6z=45
3x-7y +4z=-7
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22y-10z=52
60y-10z=90
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-38y =-38
y=1
6(1) -z=9
6-z=9
-z=9-6=3
z=-3
2x+4(1)-3(-3)=21
2x+4+9=21
2x=21-4-9=8
x=4
y=1
z=-3