# How do you find the values of x and y given [(y), (x)]=[(2x-1), (y-5)]?

Feb 9, 2017

$x = 6 , \mathmr{and} , y = 11.$

#### Explanation:

From the Defn. of Equality of Matrices, we have,

$\left(1\right) : y = 2 x - 1 , \mathmr{and} , \left(2\right) : x = y - 5$.

$\text{Substituting "y" from "(1)" into "(2)," we get,}$

$x = \left(2 x - 1\right) - 5 = 2 x - 6.$

$\therefore x - 2 x = - 6 , i . e . , x = 6.$

Then, by $\left(1\right) , y = 2 \left(6\right) - 1 = 11.$

Thus, $x = 6 , \mathmr{and} , y = 11.$