Answer
$x=\left(-\dfrac{17}{2},\dfrac{11}{4}\right)$
Work Step by Step
We are given:
$x=(a,b)$
$u=(2,-3)$
$v=(-4,1)$
$-4x=u-8v$
Substitute the expressions of the vectors in the equation:
$-4(a,b)=(2,-3)-8(-4,1)$
$(-4a,-4b)=(2,-3)-(-32,8)$
$(-4a,-4b)=(2+32,-3-8)$
$(-4a,-4b)=(34,-11)$
Determine $a,b$:
$\begin{cases}
-4a=34\\
-4b=-11
\end{cases}$
$a=-\dfrac{34}{4}=-\dfrac{17}{2}$\\
$b=\dfrac{-11}{-4}=\dfrac{11}{4}$
The solution is:
$x=\left(-\dfrac{17}{2},\dfrac{11}{4}\right)$
