# How do you solve the system by the substitution method: 2x+3y=6,x=y-7?

Nov 14, 2016

$x = - 3 \mathmr{and} y = 4$

#### Explanation:

color(blue)(x = (y-7))" larr this means that $x \mathmr{and} \left(y - 7\right)$ are identical.
They are therefore interchangeable and one can replace the other.

$\text{ "2color(blue)(x) +3y =6" } \leftarrow$ replace x with $\textcolor{b l u e}{\left(y - 7\right)}$
$\textcolor{w h i t e}{\ldots \ldots} \downarrow$
$2 \textcolor{b l u e}{\left(y - 7\right)} + 3 y = 6 \text{ } \leftarrow$ only y as a variable

$2 y - 14 + 3 y = 6$

$5 y = 6 + 14$

$5 y = 20$

$y = 4 \text{ } \leftarrow$ if you know $y$, you can work out $x$

$x = y - 7$

$x = 4 - 7 = - 3$

Check:
$2 x + 3 y = 2 \left(- 3\right) + 3 \left(4\right)$

$= - 6 + 12 = 6 \text{ } \leftarrow$ which is correct.