Question

Find the value of $y-x$ from the following equation:$2\left[\begin{array}{cc}x& 5\\ 7& y-3\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]$

• (A) $7$
• (B) $-7$
• (C) $6$
• (D) $-6$

Answer 1

The Correct Option is A

Explanation:
Given,$\begin{array}{r}2\left[\begin{array}{cc}x& 5\\ 7& y-3\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]\end{array}$$\begin{array}{r}\Rightarrow \left[\begin{array}{cc}2x& 10\\ 14& 2y-6\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]\end{array}$$\begin{array}{r}\Rightarrow \left[\begin{array}{cc}2x+3& 6\\ 15& 2y-4\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]\end{array}$As we know that,If two matrices $A$ and $B$ are equal then their corresponding elements are also equal.$\therefore 2x+3=7$$\Rightarrow 2x=7-3$$\Rightarrow 2x=4$$\Rightarrow x=2$And $2y-4=14$$\Rightarrow 2y=14+4$$\Rightarrow 2y=18$$\Rightarrow y=9$Now,$y-x=9-2=7$So, the value of $y-x$ is $7$.Hence, the correct option is (A).