# What is the solution of the system y=x-10, y=2x+5?

Nov 12, 2016

$x = - 15 \mathmr{and} y = - 25$

#### Explanation:

This is a perfect scenario for solving the two equations.
(which represent straight lines and the solution gives the point of intersection.)

$\textcolor{b l u e}{y = x - 10} \text{ and } \textcolor{red}{y = 2 x + 5}$

The two $y -$ values are equal!

$\textcolor{w h i t e}{\times \times \times \times \times \times x} \textcolor{b l u e}{y} = \textcolor{red}{y}$

Therefore:$\textcolor{w h i t e}{\times x} \textcolor{b l u e}{x - 10} = \textcolor{red}{2 x + 5}$

$\textcolor{w h i t e}{\times \times . \times x} - 10 - 5 = 2 x - x$

$\textcolor{w h i t e}{\times \times . \times x} - 15 = x \text{ } \leftarrow$ we have the x-value

$y = \left(- 15\right) - 10 = - 25 \text{ } \leftarrow$ from the first equation

Check in the second equation:

$y = 2 \left(- 15\right) + 5 = - 25$

$x = - 15 \mathmr{and} y = - 25$