# How do you find the values of x and y given [(2y), (x)]=[(x-3), (y+5)]?

Dec 1, 2016

I found $x = 7 \mathmr{and} y = 2$

#### Explanation:

For the two column matricesto be equal we need that:
$2 y = x - 3$
$x = y + 5$
so we substitute the second into the first for $x$:
$2 y = y + 5 - 3$
rearrange:
$y = 2$
substitute back into the secnd:
$x = 2 + 5 = 7$

Dec 1, 2016

$x = 7 \text{ and } y = 2$

#### Explanation:

When 2 matrices are equal then.

$\textcolor{b l u e}{\text{the x-components are equal and the y-components are equal}}$

$\Rightarrow 2 y = x - 3 \leftarrow \text{ x-components}$

and $x = y + 5 \leftarrow \text{ y-components}$

Substitute x = y + 5 into the x-components equation.

$\Rightarrow 2 y = y + 5 - 3 \Rightarrow y = 2$

$\text{ and } x = 2 + 5 = 7$