This lesson on simultaneous equations will concentrate on solving two equations for two pronumerals: X and Y.

The technique of solving simultaneous equations by the substitutions method is best shown through examples. Here’s the first one. We have to solve this pair of simultaneous equations using the substitution method.

Y=X-3, and 2X+Y=9.

What we want to do is to create one equation with one unknown to solve. In the substitution method, we have a choice of whether to make a substitution for X or a substitution for Y. It will depend in each case which is the easier way to do it. Looking at these two equations, it would be much easier to substitute for Y than X. As the substitution is quite straight forward, Y is the subject in our first equation. Because the right side of the first equation is equal to Y, we can substitute the expression X-3 into the second equation in the place of the Y term. This will give us 2X+(X-3)=9. The brackets have been put in to highlight the substitution.

Look closely at how this substitution occurred. We have placed the X-3 into the position where Y was. This has left us with an equation where we only have to solve for X. Simplify the left hand side of the equation, and we have 3X-3=9. Add 3 to the 9, and this become 3X=12, and dividing both sides of the equation by 3, we have X=4.