# How do you solve y = -x + 5 and 2x - 3y = -6 using substitution?

Mar 17, 2016

$\left(\frac{9}{5} , \frac{16}{5}\right)$

#### Explanation:

As given by the first equation, we see that $\textcolor{red}{y = - x + 5}$. Because of this, we can plug color(red)(-x+5 in for $\textcolor{red}{y}$ in the second equation.

$2 x - 3 \textcolor{red}{y} = - 6 \text{ "=>" } 2 x - 3 \left(\textcolor{red}{- x + 5}\right) = - 6$

When distributing $- 3$ into $\left(- x + 5\right)$, note that the negative will change the signs of the terms in the parentheses, so:

$- 3 \left(\textcolor{b l u e}{-} x \textcolor{b l u e}{+} 5\right) = \textcolor{g r e e n}{+} 3 x \textcolor{g r e e n}{-} 15$

So, we have

$2 x + 3 x - 15 = - 6$

$5 x - 15 = - 6$

$5 x = 9$

color(purple)(x=9/5

With this, we can plug this value for $x$ into either equation. I'll choose the first, since it's simpler:

$y = - \textcolor{p u r p \le}{x} + 5 \text{ "=>" } y = - \textcolor{p u r p \le}{\frac{9}{5}} + 5$

Find a common denominator:

$y = - \frac{9}{5} + \frac{25}{5}$

$\textcolor{b r o w n}{y = \frac{16}{5}}$

Since we have color(purple)(x=9/5 and $\textcolor{b r o w n}{y = \frac{16}{5}}$, our final answer is the ordered pair $\left(\textcolor{p u r p \le}{\frac{9}{5}} , \textcolor{b r o w n}{\frac{16}{5}}\right)$.