# How do you solve 2x + 7y = 30 and x = 48 - 9y using substitution?

May 11, 2016

$y = 6$

#### Explanation:

$2 x + 7 y = 30 \text{ " and " } \textcolor{red}{x = 48 - 9 y}$

Remember that the = sign tells us that two expressions are absolutely the same as each other - specifically that they are inter-changeable! In these equations: $\text{x IS THE SAME AS (48 - 9y)}$.

So, in the first equation an $x$ can be replaced by (48 - 9y).

$2 \textcolor{red}{x} + 7 y = 30 \text{ } \Rightarrow 2 \textcolor{red}{\left(48 - 9 y\right)} + 7 y = 30$

$2 \left(48 - 9 y\right) + 7 y = 30$
$96 - 18 y + 7 y = 30$
$96 - 30 = 18 y - 7 y$

$66 = 11 y$

$6 = y$