Question

Find X if $2X+3Y=\left[\begin{array}{cc}2& 3\\ 4& 0\end{array}\right]and3X+2Y=\left[\begin{array}{cc}7& -2\\ -1& 5\end{array}\right]$

• A. $\left[\begin{array}{cc}\frac{-2}{5}& \frac{12}{5}\\ \frac{11}{5}& -3\end{array}\right]$
• B. $\left[\begin{array}{cc}\frac{2}{5}& \frac{-12}{5}\\ \frac{-11}{5}& 3\end{array}\right]$
• C. $\left[\begin{array}{cc}\frac{2}{5}& \frac{13}{5}\\ \frac{14}{5}& -2\end{array}\right]$
• D. $\left[\begin{array}{cc}\frac{-2}{5}& \frac{-13}{5}\\ \frac{-14}{5}& 2\end{array}\right]$

Answer 1

The correct option is B

$\left[\begin{array}{cc}\frac{2}{5}& \frac{-12}{5}\\ \frac{-11}{5}& 3\end{array}\right]$

$2X+3Y=\left[\begin{array}{cc}2& 3\\ 4& 0\end{array}\right]........\left(i\right)3X+2Y=\left[\begin{array}{cc}2& -2\\ -1& 5\end{array}\right]........\left(ii\right)\left(i\right)\times 2\Rightarrow 4X+6Y=\left[\begin{array}{cc}4& 6\\ 8& 0\end{array}\right]........\left(iii\right)\left(ii\right)\times 3\Rightarrow 9X+6Y=\left[\begin{array}{cc}6& -6\\ -3& 15\end{array}\right]........\left(iv\right)\left(iv\right)-\left(iii\right)\Rightarrow 5X=\left[\begin{array}{cc}2& -12\\ -11& 15\end{array}\right]x=\left[\begin{array}{cc}\frac{2}{5}& \frac{-12}{5}\\ \frac{-11}{5}& 3\end{array}\right]$