Find x and y, if [2x+y-1134y4][-1 64303]=[3556187].

Exercise 2.2 | Q 13 | Page 47

QUESTION

Find x and y, if ${\displaystyle \left[\begin{array}{ccc}2x+y& -1& 1\\ 3& 4y& 4\end{array}\right]\left[\begin{array}{ccc}-1& 6& 4\\ 3& 0& 3\end{array}\right]=\left[\begin{array}{ccc}3& 5& 5\\ 6& 18& 7\end{array}\right]}$.

SOLUTION

${\displaystyle \left[\begin{array}{ccc}2x+y& -1& 1\\ 3& 4y& 4\end{array}\right]\left[\begin{array}{ccc}-1& 6& 4\\ 3& 0& 3\end{array}\right]=\left[\begin{array}{ccc}3& 5& 5\\ 6& 18& 7\end{array}\right]}$

∴ ${\displaystyle \left[\begin{array}{ccc}2x+y-1& -1+6& 1+4\\ 3+3& 4y+0& 4+3\end{array}\right]=\left[\begin{array}{ccc}3& 5& 5\\ 6& 18& 7\end{array}\right]}$

∴ ${\displaystyle \left[\begin{array}{ccc}x+y-1& 5& 5\\ 6& 4y& 7\end{array}\right]=\left[\begin{array}{ccc}3& 5& 5\\ 6& 18& 7\end{array}\right]}$

∴ By equality of matrices, we get
2x + y – 1 = 3 and 4y = 18

∴ 2x + y = 4 and y = ${\displaystyle \frac{18}{4}=\frac{9}{2}}$

∴ ${\displaystyle 2+\frac{9}{2}}$ = 4

∴ 2x = ${\displaystyle 4-\frac{9}{2}}$

∴ 2x = ${\displaystyle -\frac{1}{2}}$

∴ x = ${\displaystyle -\frac{1}{4}}$ and y = ${\displaystyle \frac{9}{2}}$.