How To Solve Simultaneous Equations

You have the 2 equations. Y equals 2x plus 3 and y equals 4x plus 1 and you're asked to solve these simultaneous equations. Well, first of all, we need to know that when we say solve simultaneous equations, what we mean is we need a pair of values, x and y, which work in both equations.

There's 2 ways of doing this. The first way, which is really nice if you have the time or the ICT facilities is simply to plot the 2 graphs. We just plot something here.

Two graphs would look something life this.and like this. This one here, crossing at 1.this one here, not a great day, crossing at 3, and then you just read off the point where they cross. Obviously, not the most accurate diagrams but if you can draw an accurate diagram, we simply read off this coordinate and that willl give you an x and a y value that works in these 2 equations.

The way that we do it without a diagram is the following. We have to notice that both are equal to y. Both equations are equal to y, which means that not only is this and this equal to y but they are also equal to each other.

Once again, just to recap, the reason we have this is because both are equal to the same thing. The next step is just to realize that you get all the x terms on one side and all the numerical terms on the other side. So, first things first, let's get rid of this 1.

It's always a good practice to write down what it is you're doing step to step. Here, I've written down we're subtracting 1 and that is from both sides. Often ou may hear move the 1 to the other side.

It's good to understand that what you're actually doing is subtracting the 1 from both sides. 3 subtract 1 is 2. So that's where we got this from. And from this side, 1 subtract 1 is 0, so we're left with just 4x. The next step, I'll draw this again, in a different color, is to take this 2x away.

Now what we have on this side, because 2x minus 2x is 0, is 2 equals 4x minus 2x, which is 2x. and the final step to find the x value is to realize that we just need to get rid of this 2 here. So what we do is divide by 2.

This gives us 1 on the left hand side and just x on the right hand side. and now we have an x value that will work in both. Now, let's find the y value that corresponds to this x.

I'm just going to remove this work in here and remember that x was equal to 1. What we simply do is substitute this into either of the equations. Y equals 2, 1 for x plus 3.

so y is equal to 2 because 2 times 1 is just 2 plus 3, which is equal to 5. So, the 2 coordinates, which works for both equations is (1,5) and this is the solution for the simultaneous equation. and that's how to solve simultaneous equations. .