A first degree equation in two variables is known as a linear equation in two variables. The equation contains two variables without exponents. Examples are:

$x-2y = 8$

$y = -3x + 5$

$C=2\pi r$

A single linear equation in two variables can be solved literal for one variable in terms of the other. A common solution for a system of linear equations consisting of two equations with the same two variables can be found if it exists using algebraic and graphing methods.

$x-2y = 8$

$y = -3x + 5$

$C=2\pi r$

A single linear equation in two variables can be solved literal for one variable in terms of the other. A common solution for a system of linear equations consisting of two equations with the same two variables can be found if it exists using algebraic and graphing methods.

## Different forms of a linear equation

- General form $ax+by+c=0$ Example: $2x-3y+5=0$
- Standard form $ax+by=c$ Example: $3x+5y=10$
- Slope-Intercept form $y=mx+b$ Example: $y=-2x+7$
- Point-slope form $y-y_{1}=m(x-x_{1})$ Example: $y-3=\frac{2}{3}(x-6)$

## Solving a linear equation in slope intercept form

Example: Write the equation $x+2y=4$ in slope intercept form.

The equation is given in standard form. To write the equation in the standard form, we need to isolate the dependent variable y on one side of the equation.

$x+2y = 4$

$-x -x$ Subtraction Property of Equality

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$2y = -x + 4$

$\frac{2y}{2} =\frac{-x+4}{2}$ Division Property of Equality

$y=\frac{-x}{2}+2$ Equation solved in slope intercept form.

Equations given in other forms can also be solved to slope intercept in a similar manner.

## Solving a system of Linear equations in two variables.

- Consistent System: The system may have a unique numeric solution or infinitely many solutions.
- Inconsistent system: The system does not have a solution. In this case, the graphs of two equations are parallel straight lines.

For a consistent system with many solutions the graphs of the two equations will be coincident, thus all the points on the straight line are solutions to the system. The system of linear equations is then known as a dependent system.