5x + 14y - 2z = -36 7x + 3y + 4z = 22 3x - 2y - Z= 9

Question 1

Question 2

Answer:

$=(774)/(337),\:z=(1225)/(337),\:y=-(968)/(337)$

Explanation:

Given:

$\begin{bmatrix}5x+14y-2z=-36\\ 7x+3y+4z=22\\ 3x-2y-z=9\end{bmatrix}$

Solve:

$\mathrm{Substitute\:}x=(-36-14y+2z)/(5)$

Thus,

$\begin{bmatrix}7\cdot (-36-14y+2z)/(5)+3y+4z=22\\ 3\cdot (-36-14y+2z)/(5)-2y-z=9\end{bmatrix}$

Simplify

$\begin{bmatrix}(-83y+34z-252)/(5)=22\\ (-52y+z-108)/(5)=9\end{bmatrix}$

$\mathrm{Substitute\:}y=-(-34z+362)/(83)$

$\begin{bmatrix}(-52\left(-(-34z+362)/(83)\right)+z-108)/(5)=9\end{bmatrix}$

Simplify

$\begin{bmatrix}(-337z+1972)/(83)=9\end{bmatrix}$

$\mathrm{For\:}y=-(-34z+362)/(83)$

$\mathrm{Substitute\:}z=(1225)/(337)$

$y=-(-34\cdot (1225)/(337)+362)/(83)$

y=-(968)/(337)

$\mathrm{For\:}x=(-36-14y+2z)/(5)$

$\mathrm{Substitute\:}z=(1225)/(337),\:y=-(968)/(337)$

$x=(-36-14\left(-(968)/(337)\right)+2\cdot (1225)/(337))/(5)$

x=(774)/(337)

Therefore, the solutions are:

$=(774)/(337),\:z=(1225)/(337),\:y=-(968)/(337)$

~lenvy~

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