Matrices - Find x, y and z

Question

I have two matrices $A$ and $B$ and I'm trying to figure out what $x$, $y$, and $z$ are.

$$\begin{bmatrix}x+2y&x\\-x+y&2x-y\end{bmatrix} = \begin{bmatrix}10&2x-3y\\-4&10\end{bmatrix}$$

What I have so far is:

$x + 2y = 10$

$-x+y= -4$

$x=2x-3y$

$2x-y = 10$

I don't know how to proceed on from here as each equation has two unknowns. I'm really bad at algebra so any help would be much appreciated!

I also do not have any idea why the question asks to find $z$ as there is no $z$ variable to work with.

Answer 1

Adding the first and second equations yields

$$ 3y = 6 \Longrightarrow y = 2$$

Not put $y=2$ in the second equation and you will get $$-x + 2 = -4 \Longrightarrow x = 6$$

Now you have to check, if for those values of $x$ and $y$ the 3rd and 4th equation is fulfilled as well,

Answer 2

From the third equation, you get $x = 3y$, from the first you get $y=2$, and so you get $x = 6$.