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Hi, I'm Mrs Dennett.

And in today's lesson, we're going to be solving linear simultaneous equations, where one of the coefficients is equal.

We're going to start this lesson with a couple of questions to really get you thinking.

Pause the video to complete this task and restart when you finished.

Here are the possible pairings for x and y.

Did you manage to find them all? If you do this methodically, starting with x equals one and then x equals two, you shouldn't miss any out.

Did any of you include zero and six? zero is a neutral integer.

It's neither positive nor negative.

So it's not included here.

The next question shows a picture of two equations.

Can you work out the value of the triangles Pause the video to give yourself some thinking time and restart when you think you have an answer.

Here is the answer.

There is a difference of one green triangle and four yellow circles between these two equations.

So one green triangle is with four yellow circles.

We can use this to work out the second equation, two blue triangles are worth two yellow circles.

So one blue triangle is worth one yellow circle.

We're going to consider the previous question using algebra.

Green Triangle is going to be represented by x.

blue triangle is going to be represented by y.

We can rewrite the pictures using algebra.

So the first equation will be two x plus two y equals 10.

where two x is the two green triangles, two y is the two blue triangles, and 10 represents the 10 yellow circles.

We can do the same for the second equation, we get x plus two y equals six.

We label the equations clearly to help us identify them.

I've chosen to label them A and B.

Look carefully at the equations.

If we want to find the values of x and y, we have to solve them simultaneously.

That means finding the values of x and y.

both equations have the same number of y's.

There is two y in each equation.

We call this number the coefficient.

In this example, both equations have a coefficient of positive two for the y's.

We want to eliminate this two y term from the equations So that we can find the value of x.

In order to do this, we have to use subtraction, we subtract equation B from equation A.

So we do two x take away x, which leaves us with x, two y, take away two y, which leaves us with zero, and 10 take away six, which gives us four we have worked out that x is equal to four.

This can be used to help us to find y we substitute x equals four into one of the original equations.

I've chosen equation B, because it looks like it's going to be more efficient to substitute x into it I replace the x with a four and solve as you would with any linear equation.

Taking four from both sides and then dividing by two, We get y equals one we can check the values for x and y in the first equation, equation A.

So two times four is eight, add two times one, which is two, and eight, add two gives us 10.

So we know that our values are correct, x equals four, and y equals one.

Here are some questions for you to try.

Pause the video to complete the task and restart the video when you finished.

Here are the answers.

All of these questions require subtraction of one equation from another in order to eliminate one of the letters.

Part C and D need extra special attention as both y terms and W terms are negative.

Remember, that subtracting a negative is like adding We're now going to look at solving simultaneous equations using addition, again, labelling each equation helps us to easily identify them.

You may notice that this time was both equations have coefficient of two in the y terms, one is negative and the other term is positive.

How can we eliminate the y terms to help us find x in this case, this time we use addition.

Adding the two equations together will eliminate the y's.

So we do five x add three x to give us eight x two Y, add negative two y, which gives us zero and 11 add 13 which gives us 24.

Remember, we want to eliminate the y's so we need to make zero with these terms. We get eight x plus zero equals 24.

No y terms. Now we can solve to find x, so we divide both sides by eight to get x equals three.

We now want to find the value of y.

So we substitute x equals three into one of the original equations.

I've chosen equation A, we now solve it.

So five times three gives us 15,add two y equals 11.

Take care when subtracting this 15 from both sides of the equation 11 takeaway 15 gives us negative four, so y will be negative two.

A useful strategy at this point is to check your solutions for x and y in the other equation, equation B.

We can see that we do get 13 so we can be sure other solutions are correct.

So x equals three and y equals negative two.

Here are some questions for you to try.

Pause the video to complete these tasks and restart when you will finished.

Here are the answers.

before when we have the same signs for the terms that we wanted to eliminate, we always subtracted this time we have different signs, one positive and one negative.

So to eliminate these terms, we have to add them.

D was quite tricky to solve because of all the negative terms. When you add the equations together, to eliminate the Z terms, you get minus nine y equals minus 45 dividing minus 45 by minus nine gives positive five I hope you get used to this method.

There are lots of steps involved.

But the more you practise, the quicker and more accurate you will become use small questions for you to try pause the video to complete the task and restart when you finished.

here are the answers.

Did you notice that because both pairs of letters have the same coefficient, you could have solved these simultaneous equations by addition or subtraction.

I definitely prefer to use an addition though, but you could challenge yourself to try both methods and check that you get the same solutions.

In this final question, you will need to form two linear equations for Samis order and for James' order before you solve them simultaneously.

Pause the video and resume Once you are finished.

Here is the answer.

You needed to form two equations here.

I used f for fish and c chips.

The equation for samis' order, is three f plus four c equals 16.

80 for James' is order, the equation is eight f plus four c equals 36.

80 We subtract the Four c terms because they have the same sign.

So five fish cost 20 pounds.

Therefore one fish would cost four pounds and we can find the cost of the chips using subtraction.

Chips cost 1.

20 so one fish and one chips is 5.

20 this question made me really hungry.

I'm glad it's the last one.

That's all for this lesson.

Remember to take the exit quiz before you leave.

Thanks for watching.