# How do you solve the following system?:  2x - y = 6 , x = 1/2y + 3

Sep 3, 2016

There is only one equation and it cannot be solved - there are infinitely many solutions for an equation with 2 variable.

#### Explanation:

With simultaneous equations there are three basic approaches:

1. Try to make additive inverses with one of the variables - so that the term is positive in one of the equations and negative in the other. Adding the equations will eliminate the terms that are additive inverses.
2. Make one of the variables the subject of one of the equations. You can then substitute for that variable in the other equation.

3.$\textcolor{red}{\text{ Make the same variable the subject of each equation}}$
$\textcolor{red}{\text{ - you can then equate the other sides of the equations.}}$

$\textcolor{red}{x} = \frac{1}{2} y + 3 \text{ and } 2 \textcolor{red}{x} - y = 6$
$\textcolor{red}{x} = \frac{1}{2} y + 3 \text{ and } \textcolor{red}{x} - \frac{1}{2} y = \frac{6}{2}$
$\textcolor{red}{x} = \frac{1}{2} y + 3 \text{ and } \textcolor{red}{x} = \frac{1}{2} y + 3$

Looking at the two equations we see they are the same equation, just given in different forms.

There is no single solution for an equation with 2 variables - there are infinitely many solutions.

For each chosen value of x there will be a y-value.