# How do you find the values of x and y given [(18, 24)]=[(4x-y, 12y)]?

May 10, 2017

$x = 5$ and $y = 2$

#### Explanation:

$\left[\left(18 , 24\right)\right] = \left[\left(4 x - y , 12 y\right)\right]$ means that the given two $1 \times 2$ matrices are equal.

Any two matrices are equal only if each element of one matrix is equal to the corresponding element of other matrix.

Hence, here we have $18 = 4 x - y$

and $24 = 12 y$

The second equation gives us $y = \frac{24}{12} = 2$

and hence first equation reduces to

$18 = 4 x - 2$ or $4 x = 18 + 2 = 20$ and $x = \frac{20}{4} = 5$

Hence, $x = 5$ and $y = 2$.