# How do you solve the system X+y=10 and 5x-y=8?

Feb 12, 2017

See the entire solution process below:

#### Explanation:

Step 1) Solve the first equation for $x$:

$x + y = 10$

$x + y - \textcolor{red}{y} = 10 - \textcolor{red}{y}$

$x + 0 = 10 - y$

$x = 10 - y$

Step 2) Substitute $10 - y$ for $x$ in the second equation and solve for $y$:

$5 x - y = 8$ becomes:

$5 \left(10 - y\right) - y = 8$

$\left(5 \times 10\right) - \left(5 \times y\right) - y = 8$

$50 - 5 y - y = 8$

$50 - 6 y = 8$

$- \textcolor{red}{50} + 50 - 6 y = - \textcolor{red}{50} + 8$

$0 - 6 y = - 42$

$- 6 y = - 42$

$\frac{- 6 y}{\textcolor{red}{- 6}} = - \frac{42}{\textcolor{red}{- 6}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 6}}} y}{\cancel{\textcolor{red}{- 6}}} = 7$

$y = 7$

Step 3) Substitute $- 7$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = 10 - y$ becomes:

$x = 10 - 7$

$x = 10 - 7$

$x = 3$

The solution is: $x = 3$ and $y = 7$ or $\left(3 , 7\right)$