What is a Linear Equation?

• A linear equation is an equation between two variables that gives a straight line when plotted on a graph.
• Here are 2 simple examples of linear equations:   5x=6+3y       or     y=2x+1
• Here is an example of a linear equation that has been plotted on a graph:

•  Linear equations can contain variables that are whole numbers, integers, decimals and fractions. When dealing with linear equations that have fractions, the best way to solve it is to find a common denominator.

How can Equations be Modelled Using Algebra Tiles?

If you don’t have algebra tiles you can always draw out and solve the equation by drawing the tiles on paper. I did not have tiles so below I visually represented how I solved the linear equation.

• When using algebra tiles, coloured tiles are positive integers and non-coloured tiles (white tiles) are negative integers.
• Larger coloured rectangular tiles are used as 1x and the smaller coloured squares are used for 1.
• Larger non-coloured rectangular tiles are used as negative 1x and the smaller non-coloured squares are used for negative 1.
• See photo below:

This is an example of how I visually solved the equation below. I drew it out using algebra tiles.

How to Solve Equations Algebraically?

To solve the following simple algebraic equation I have get x all by itself. We call that isolating the variable.

If you have the equation:      2x+3=7

• I want to get x alone. The first step would be to get rid of the +3 by subtracting 3 (this cancels each other out). I remember that what I do to one side of the equation, I have to do to other so I subtract 3 from 7. Now, I’m left with 2x= 4
• to isolate the x I divide 2 by 2 to cancel each other out (which leaves me with x on its’ own). What I do to one side, I do to the other so I divide 4 by 2 and I get the answer x=2