# How do you solve the system x=10 +5y and 2x-10y=20?

Jun 9, 2018

x;(x-10)/5

#### Explanation:

Dividing the second equation by $2$ we get

$x - 5 y = 10$
or
$x = 10 + 5 y$
this equation is identical to the first one.

Jun 9, 2018

There are many solutions because the two equations are just different forms of the same equation.

#### Explanation:

The equations given do not represent a system of equations because the one is just a different form of the other.

$2 x - 10 y = 20$ if divided by $2$ gives $x - 5 y = 20$ which is the same as $x = 10 + 5 y$

There is no single or unique for an equation which has two variables, but rather there are infinitely many solutions.

In this case, any value can be chosen for $y$ and the corresponding $x$ value can be determined.

A few possible solutions are:

$\left(10 , 0\right) \text{ "(20,2)" "(25,3)" } \left(60 , 10\right)$ and so on.