Question

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Find the values of x and y, if​
$\left[\begin{array}{c}3\text{x}-\text{y}\\ 5\end{array}\right]=\left[\begin{array}{c}7\\ \text{x}+\text{y}\end{array}\right]$

Answer 1

Given:
$\left[\begin{array}{c}3\text{x}-\text{y}\\ 5\end{array}\right]=\left[\begin{array}{c}7\\ \text{x}+\text{y}\end{array}\right]$

Two matrices are equal, if their corresponding elements are equal.

$3\text{x}-\text{y}=7$-(i)
$\text{x}+\text{y}=5$-(ii)


On adding both the equations,
$4\text{x}=12$

$\text{x}=\frac{12}{4}$

$\text{x}=3$

Put the value of x in eq (ii),

$3+\text{y}=5$
$\text{y}=5-3$
$\text{y}=2$

Hence, the values of x and y are $3$ and $2$ respectively.