Answer
$x=\left(\dfrac{4}{3},-\dfrac{11}{3}\right)$
Work Step by Step
We are given:
$x=(a,b)$
$u=(2,-3)$
$v=(-4,1)$
$3x-4u=v$
Substitute the expressions of the vectors in the equation:
$3(a,b)-4(2,-3)=(-4,1)$
$(3a,3b)-(8,-12)=(-4,1)$
$(3a-8,3b+12)=(-4,1)$
Determine $a,b$:
$\begin{cases}
3a-8=-4\\
3b+12=1
\end{cases}$
$\begin{cases}
3a=-4+8\\
3b=1-12
\end{cases}$
$\begin{cases}
3a=4\\
3b=-11
\end{cases}$
$a=\dfrac{4}{3}$
$b=-\dfrac{11}{3}$
The solution is:
$x=\left(\dfrac{4}{3},-\dfrac{11}{3}\right)$
