If an equation has a single unknown, we can usually solve it


x + 5 = 15 x = 10

However if an equation has two unknowns, it is usually impossible to solve.


3x + 4y = 22

There are infinite combinations of x and y that could be substituted into this equation to give 22, and so there is no single solution for the value of x and y.

For example, substituting the following into the equation will all produce 22

x = 0, y = 5.5

x = 22/3, y = 0

x = 2, y = 4

If we are provided with a second equation, however, then there will be only a single solution (if both equations are linear)

3x + 4y = 22

-2x + 4y = 12

There is now only a single solution for x and y that will produce both 22 in the first equation, and 12 in the second: x = 2, y = 4.

To solve the simultaneous equations graphically is fantastically easy to solve

Plot the two equations See where they cross – the coordinates where the two graphs cross are the solutions for x and y

The graphs will cross only once if both are linear. If one of them is non-linear, then they may cross once, twice, or sometimes not at all.

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