Find the vector that meets the following criteria

Question

I want to find the vector $X$ by the following lines:
$$(1,-3,5) \cdot X=49$$ $$(4,1,-1) \cdot X = 0$$ $$(2,0,-3)\cdot X=-9$$ I would like to get some advice how to find him.
Thanks!

Answer 1

Hint: Assume the vector $X=(x,y,z)$ and then solve the system of equations.

Answer 2

$b=\begin{pmatrix}49\\0\\-9\end{pmatrix}$,

$A=\begin{pmatrix}1&-3&5\\4&1&-1\\2&0&-3\end{pmatrix}$,

$x=A^{-1}*b$

$So, x=\begin{pmatrix}3\\-7\\5\end{pmatrix}$.