Solving simultaneous equations

A linear equation with a single unknown is relatively straightforward to solve. For example

x + 7 = 11

We can subtract 7 from both sides to give the answer x = 4.

However, if there are two unknowns, such as

x + y = 4

there are various of values of x and y that will satisfy the equation. In this case we could have x = 0 and y = 4; x = 1 and y = 3; x = y = 2; x = 3 and y = 1; or x = 4 and y = 0. There are also an infinite number of non-integer answers. To find the values of x and y we need more information.

Let’s suppose we are also told that

x – y = 2

These two equations are known as simultaneous equations because they are true simultaneously. In general, we need as many equations as we have variables to be able to determine their values.

Paul Yates discusses how to solve simultaneous equations and their applications.