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# Simultaneous Equations... watch

1. Hello

I came across this question:

y = 10 - x
y = 2x^2 + 4

This is what I have done:

10 - x = 2x^2 + 4 (10 + x)
0 = 2x^2 + x - 6

Use the formula and get
x = 1.5
x = -2

I then plug these back into the equations to find Y

10 - - 2 = 12
2 x 1.5^2 + 4 = 8.5

But I then also found that it works either way, i.e

10 - 1.5 = 8.5
2 x -2^2 + 4 = 12

So my question is, how would I know how to pair them up properly.

The markscheme says that you get an extra mark for 'pairing them correctly' and the correct pairs are

10 and - 2
1.5 and 12

I'm probably missing something obvious as always but I wouldn't know how to 'correctly' pair them?

Thanks
2. It means when you put one of the x values into any of the original equation you will get a corresponding y value. This is how you know which one pairs with the other one!
3. Thats what I did

my X values are -2 and 1.5

So when I put them back into the equation I get

Y = 10 - - 2 = 12
Y = 2 x 1.5^2 + 4 = 8.5

But then I can put them the other way round and get

Y = 10 - 1.5 = 8.5
Y 2 x -2^2 + 4 = 12

I am not given a Y value so I just don't know how I would know which way they go around? Its hard to explain
4. (Original post by Tinkletea)
Thats what I did

my X values are -2 and 1.5

So when I put them back into the equation I get

Y = 10 - - 2 = 12
Y = 2 x 1.5^2 + 4 = 8.5

But then I can put them the other way round and get

Y = 10 - 1.5 = 8.5
Y 2 x -2^2 + 4 = 12

I am not given a Y value so I just don't know how I would know which way they go around? Its hard to explain
You're confusing yourself!

The simpler of the 2 equations you start with is y = 10 - x. So once you've found your 2 possible x values, put them into this equation in turn to get the corresponding y value
5. STOP
Same symbol Take away Opposite symbol Plus this is what i remember from IGCSE dunno if it will help althou its quite cute
6. I'm not making myself clear, sorry. My question is yes I have two x values 1.5 and -2. You say to put them into the equation, but I have two X values, how would i know which one would go into the first bit of the equation (10 - x) and which one goes into the second part (2x^2 + 4), so would I do (10 - - 2) or (10 - 1.5) ???

I'm obviously missing something simple but I just dont know which one I need to put into the first part (10 - x) since I am not told what Y is. Its not like it says 12 = 10 - x for example, it just says Y = 10 - x

Thanks
7. (Original post by Tinkletea)
I'm not making myself clear, sorry. My question is yes I have two x values 1.5 and -2. You say to put them into the equation, but I have two X values, how would i know which one would go into the first bit of the equation (10 - x) and which one goes into the second part (2x^2 + 4), so would I do (10 - - 2) or (10 - 1.5) ???

I'm obviously missing something simple but I just dont know which one I need to put into the first part (10 - x) since I am not told what Y is. Its not like it says 12 = 10 - x for example, it just says Y = 10 - x

Thanks

You do not put one x value in one equation and the other in the other

You choose an equation

So
x=-2
y=10--2 = 12

So one pair is x=-2, y=12

And
x=1.5
y=10-1.5 = 8.5

So the other pair is x=1.5, y=8.5

Note, I chose to use y=10-x to get both

I could have used y=2x^2 + 4 for both if I had wanted to

Note, you are told what y is y is 10-x

Or, alternatively y is 2x^2+4
8. Ah I get it now, thanks!

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