Simultaneous Linear Equations

Simultaneous Linear Equations

Author: Andrew Watson
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Linear equations solved graphically

The image above shows the three different solution sets that can be achieved when two linear equations are graphed. From this image you should be able to work out the relationships between gradients and y-intercepts in each case.

Using sliders to change gradient and y-intercept

Desmos graphing demonstration to illustrate concepts of different solution sets.

Sets of simultaneous equations using matrices

Using the determinant to identify number of solutions

1H - Solving Sets of Simultaneous Equations

Illustrating that if equations are rearranged to y=mx + c format then by inspecting the gradients and y-intercepts we can determine how many solutions there will be.

1H - Solving systems of equations Board 1

1H - Solving systems of equations Board 2

1H - Solving systems of equations Board 3

Using the CAS to solve systems of Equations - Part 1

Part 1 gives you the CAS commands and resulting output when trying to solve two equations that have no unique solution (parallel lines).

Using the CAS to solve systems of Equations - Part 2

As per Part 1 - this time with coincident lines and infinite solutions.