Lesson video

Hi, this is Ms. Bridgett.

And in today's lesson, we're going to look a little bit more closely about how to eliminate the variable.

You're going to need to pen.

You're going to need some paper.

As usual, you're going to need to remove any distractions.

Okay.

Let's go.

Have a look at the pair of simultaneous equations on the screen.

Within each pair, what happens if you add the equations? What happens if you subtract them? Have a look at your answers.

What's the same and what's different.

Pause the video now and have a try.

Okay.

Let's look at what happens when we add the two equations on the left together.

So adding the left hand side and the right hand side, we get 6x plus 6y is equal to 50.

If I subtract them, something slightly different happens.

I get 2x plus no y is equal to 10.

2x is equal to 10.

The y has it been eliminated.

Now in the equations on the right, something different happens.

If we subtract them, we get 6x is equal to 50, y's were eliminated.

If we subtract them, we get 2x subtract 6y is equal to 10.

Now something different has happened here.

On the left hand side, we eliminated the y by subtracting the equations.

With the equations on the right, we eliminated the y's by adding.

Now the reason that the y's have been eliminated in both cases is because the absolute value of the coefficient of y is the same.

Let's just take a closer look at this.

Now this process is called elimination.

So far, the way we've been solving simultaneous equations is to eliminate one of the variables to leave us with an equation with just one unknown in it.

Now in this top set of equations, the way that we eliminated one of the unknowns was to subtract them.

Just look at the difference between them.

In the second set of equations, the way that we eliminate one of the variables is to add them.

So what we need to be able to do is to look closely at the equations, to look for a coefficient with the same absolute value, and to decide whether or not we're going to add them together or subtract them together, to eliminate one of those unknowns.

Have a look at the pairs of simultaneous equations below.

Within each pair, decide which unknown can be eliminated.

And then I'd like you to sort them into two categories.

Those where an unknown can be eliminated by adding the equations together and those where the unknown can be eliminated by subtracting the equations.

You do not need to solve the equations.

So all you're doing is deciding which unknown is going to be eliminated and whether we can do that by adding the equations or subtracting the equations.

So pause the video now and off you go.

Okay.

Let's have a look at some of the answers.

So if we start with the top left, the coefficients of y are the same.

So we can subtract these equations.

Five y subtract five y is going to eliminate the y.

We have a look at the second equation, the absolute values of the coefficient of the y are the same.

So again, we can eliminate the y's.

But this time subtracting them would not eliminate them.

Instead, we have to add them.

Moving onto the third equation.

I've rewritten that very bottom equation.

So the bottom equation at the moment says 32 equals 4x subtract 3y.

I've rewritten that as 4x subtract 3y is equals to 32 because that helps me to compare those two equations more easily.

From there I can see that adding those equations together wouldn't make a difference to eliminating the y.

It'll leave me with negative 6y.

Instead, I need to subtract them.

Negative three subtract negative three is going to give me zero.

On the bottom left, again, I've rewritten that bottom equation.

Negative 4x plus 5y is equal to 20.

And I've written it that way so I can line up those x's and those y's.

Now if we look at the y's, they've got different coefficients.

We're not going to be able to just eliminate the y's easily.

But if we look at the x's, we can see that the coefficient of those is the same, negative four and negative four.

Now if I was to add those, I get negative eights.

However if I was to subtract them, I get negative four subtract negative four which would be zero and the x's would be eliminated.

In the middle, I'm going to rewrite that bottom equation to 4x plus 3y is equal to 30.

Again, so I can line up the x's and the y's.

And that helps me to see which one I can eliminate.

I can't eliminate the x's easily here because those coefficients are different.

The absolute values of those coefficients are different.

But if we look at the x's, ah the y's sorry, we've got plus 3y, we've got to subtract 3y.

I can add those and the y's will be eliminated.

In the final equation, I've rewritten the top equation.

Now I've not just rewritten it, I've also rearranged it.

So I rearranged it to say 3y subtract 2x is equal 20.

Again, I've done this to help me line up those y's and those x's.

I can see now that the coefficients of y's are the same.

And I can see that I need to subtract them.

For our final test today, I've given you three equations from the same system of equations.

So these are part of the same set of simultaneous equations.

Now, if I take a equation B and I subtract it twice from equation A, I can eliminate the x.

So if I take the 2x subtract 5y equals 10 and I subtract B, and I subtract B again, what I'm going to end up with is negative 7y is equal to two.

The x has been eliminated.

What I'd like you to think about is what other combinations you can find to eliminate either the x or the y.

You can use all three equations or you can just use two of them.

Pause the video and off you go.

Okay.

As always, there are loads and loads of different answers that you might have gotten here.

So we can't possibly go through them all but maybe, just maybe, here are some of the ones that you thought of.

So I could take B and I could add it to A five times.

So five lots of B added to A would eliminate the y.

Or I could subtract B from C twice.

So equation C subtract B, subtract B, and that would also eliminate the y.

That's everything for today.

So thank you so much for all of your time and all of your effort and I will see you in the next lesson.