Math Linear equations Solving linear equations

# Solving linear equations

## One variable

The solution of linear equations with one variable is any number $x$ that satisfies the equation.

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### Tip

The solution of a linear equation can be found out by trial and error. Simply use the value with which the equation is "true".

### Example

#### Given is a linear equation

$x-8=8$

#### Use appropriate value

$x=16$
$16-8=8$
$8=8$
If you use 16 for $x$ , the equation is true.

Computationally one can solve a linear equation with an equivalent transformation.

## Two variables

The solution of linear equations with two variables is every value pair $x|y$ that satisfies the equation.

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### Tip

The solution of a linear equation with two variables can be found out by trial and error. Simply use two values with which the equation is "true".

### Example

#### Given is a linear equation with two variables

$x+y=6$

#### Use appropriate values

e. g. $x=4$ and $y=2$
$4+2=6$
$6=6$ true

If one uses for $x$ 4 and $y$ 2, the equation is satisfied. The value pair $4|2$ is a solution.
But: There are endless possibilities for $x$ and $y$.
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### Remember

A linear equation with two variables has infinite solutions.

Computationally one can solve two linear equations with two variables with one system of linear equations.