Lesson video

Hi everyone, I'm Ms. Jones.

And today we are going to be looking at representing simultaneous equations graphically again.

But this time we're going to be looking at possible, a few more patterns, thinking about the relationships between different equations and seeing different conditions and that sort of thing.

So before we can begin, please make sure as per usual, you have a pen and some paper, you try and remove any distractions from around you and try and find a nice quiet space to work if you can.

Pause the video here to make sure you've got everything ready for today's lesson.

The first thing we are going to do is have a look at what's on the screen here.

What I want to know is what is the same and what is different about the following linear equations.

Now, there are lots and lots of answers you could get for this, so just write as many as you can think of.

Also make sure you sketch the graphs of each equation on the same axis, so that we've got all four of those equations on the same graph.

Pause the video now to do that.

There are lots of things you could have written about what's the same, what's different, and this is what your graph should have looked like over here.

So we can see we've got y=2x+2, y = 9-2x, y=2, y=2x + 7 Now you may have just by looking at the equations, got some similarities and differences straight away, but it might be that some of those similarities and differences didn't come out until you draw on them and you could physically see all the similarities and differences of what they look like.

So for example, we have that y=2x+2, and y=2x-7, have the same gradient.

And you might notice actually that those lines are parallel.

y=9-2x is different because it's the only one with a negative gradient.

y=2 is different because it's the only one that's horizontal.

This is some examples of what you could have said.

And you could have also said that y=2x+2 and y=2, have the same y intercepts they intercept at y axis at the same point.

You could have said that they all intercept the x axis at different points with the exception of y=2, which again is different because it doesn't intersect the x axis at all.

There are lots of different things you could have said so well done if you've got some of the examples and especially well done, if you've got some that aren't even on there and we haven't talked about yet, that's brilliant, well done.

Not all simultaneous equations have solutions, which pairs of equations do not have a solution? Hopefully you can see on the diagram, which ones are not going to have a solution? Remember though, just because the solution isn't on the set of axes that we've drawn doesn't mean it doesn't exist.

Sometimes we draw graphs on a smaller set of axes and actually the solution is off the graph.

Remember there is lines go on infinitely long, but there are two that don't have a solution.

So pause and have a think about which two do not have a solution, no matter how long you draw those lines, which ones will not have a solution.

Good, hopefully you manage to get that y=2x+2 and y=2x-7 do not have a solution.

They will never have a solution because they will never intersect.

Those two lines, don't cross, don't meet, don't intercept because by definition they are parallel.

And the rest of them do have a point of intersection, but those two do not.

Well done, if you got those answers.

Pause the video now to complete your independent task, which is here.

So we have here, six equations.

What I would like you to do is make sure that you have drawn out each of those equations on a set of axes before you even begin.

Four those equations, we've seen before.

Hopefully you've seen them before and you've already drawn some of them out.

Then once you have drawn those, you can find some solutions and solve them simultaneously, and then answer the questions below.

So again, pause the video to make sure you have got time to complete all of those questions.

So the first question is saying these two equations have a solution where the x coordinate is negative.

So hopefully you found a few solutions for that.

There's a couple of solutions, a couple of equations we could have used for that two examples here, y=x+3, and y=2.

If you solve them simultaneously and you see on your graph, they will have a negative x coordinate.

And in fact, in this example, where the x coordinate is negative one.

And also you could have had to y=x+3 and x+2y=4 they will also intersect with a negative x coordinate, well done if you've got one of those.

Number two, says these two equations have no solution.

And hopefully you remembering from that connect task, which ones aren't going to have a solution because they will not intersect, or they are two parallel lines with the same gradient.

y=2x+1 and y=2x+7.

Number three, these two equations have a solution where x and y are opposite signs.

So one coordinate is negative and coordinators positive.

There were lots of examples for this one.

And one of them is the same as question one, y=x+3 and y=2.

But they have an x coordinator of negative one and they have a y coordinate of two.

So the x coordinate is negative and the y coordinate is positive.

Well done, if you've got one of those.

And finally, for question four, these three equations have a single solution.

So for this one, it was y=9-2x, oops, y=2x+1 and y=x+3.

They all intersected one point wherever that was.

And that gave us one solution.

Really well done, if you've got that last one, you must've joined your diagrams very accurately, so well done.

Now, what I would like you to do is have a bit of an explore by creating your own equations that satisfy those same four conditions.

So two equations that have a solution where x and y coordinates are both negative.

These two equations have no solution, two equations that have a solution where x and y are opposite signs and the three equations that have a single solution.

So experiment or think about the conditions that you need for three those to be possible and have a go at creating your own.

There's lots of different solutions that you could get.

So I'm not going to be able to give you the set answers for this one.

This is just about you experimenting and having it go.

And hopefully you can work out for yourself whether you've got them correct or not.

But if you do want to please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

And then we can see some of the answers to those questions.

Really well done for all of your hard work today, there was a lot of experimenting and a lot of work for you to do on your own, but you've done really, really well.

And you've been really independent and is so very well done and see you next time.