Answer
$x=\left(-3,2\right)$
Work Step by Step
We are given:
$x=(a,b)$
$u=(2,-3)$
$v=(-4,1)$
$2x+u=v$
Substitute the expressions of the vectors in the equation:
$2(a,b)+(2,-3)=(-4,1)$
$(2a,2b)+(2,-3)=(-4,1)$
$(2a+2,2b-3)=(-4,1)$
Determine $a,b$:
$\begin{cases}
2a+2=-4\\
2b-3=1
\end{cases}$
$\begin{cases}
2a=-4-2\\
2b=1+3
\end{cases}$
$\begin{cases}
2a=-6\\
2b=4
\end{cases}$
$a=\dfrac{-6}{2}=-3$
$b=\dfrac{4}{2}=2$
The solution is:
$x=\left(-3,2\right)$
