Question

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

Answer 1

`=(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~