Find the coordinates of the vector $\vec x =[5,0]$ relative to the basis $B$

Question

Following is a homework question. My answer $[-1,1]$ is wrong even though I already verified $(-1)[-5,-6] + [-10,-6]$ is $[5,0]$. I checked stack exchange and it seems like I have the approach. What am I doing wrong?

Edit: Fixed the typo.

Answer 1

My calculations were off. I was calculating the negative of the answer.

To solve the question, all you need to do is create two multipliers $a,b$. $$ a\cdot[-5,-6] + b\cdot[-10,-6] = [5,0]\\ -5a-10b=5 \\ -6a-6b=0 $$ which gives $$ [a,b]= [1,-1] $$