How do you find the ordered pair that is the solution of equations y= -x-5 y= x+1?

Jan 24, 2017

See the entire solution process below:

Explanation:

Step 1) Because the first equation is already solved in terms of $y$, substitute $\textcolor{red}{- x - 5}$ into the second equation for $y$ and solve for $x$:

$\textcolor{red}{- x - 5} = x + 1$

$\textcolor{red}{- x} + x - \textcolor{red}{5} = x + x + 1$

$0 - 5 = 2 x + 1$

$- 5 = 2 x + 1$

$- 5 - \textcolor{red}{1} = 2 x + 1 - \textcolor{red}{1}$

$- 6 = 2 x + 0$

$- 6 = 2 x$

$- \frac{6}{\textcolor{red}{2}} = \frac{2 x}{\textcolor{red}{2}}$

$- 3 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}}$

$- 3 = x$

$x = - 3$

Step 2) Substitute $\textcolor{red}{- 3}$ for $x$ in the first equation and solve for $y$:

$y = - \textcolor{red}{- 3} - 5$

$y = 3 - 5$

$y = - 2$