How Do We Solve Simultaneous Equations?

Simultaneous Equations can be solved algebraically or graphically. We usually start off learning how to find the two solutions for intersecting two linear graphs. Linear graphs are also called straight line graphs. In the first couple of worksheets you learn how to solve simultaneous equations using algebraic techniques. To do this you'll have to be super confident with substituing into formulae as well as rearranging equations so let's start off with a substitution warm up exercise.

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Simultaneous Equations Example 1

The example below shows the intersection of y = x + 1 with y = 2x - 1. The lines cross at the point (2,3).

Simultaneous Equations Example 2

When we solve simultaneous equations involving one linear equation and one quadratic equation then we use the substitution method. We can always solve simultaneous equations graphically. So let's look exactly what we mean by simultaneous equations. Take a look at the visual below. The blue line and the red line cross at the point (- 4, 2).

Simultaneous Equations Example 3

The simultaneous equations below cross at the point (2, 4). The straight line graph is y = x + 2. The parabola curve is the quadratic graph of y = x².