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# Simultaneous equations problems

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1. x^2 + y^2 = 25
2x - y = 5

And

x^2 + 2xy + 15 = 0
2x - y + 10 =0

I could do all the others on the worksheet but I've checked the answers for these two and still don't understand how to do them
2. For 1.
did you rearrange equation 2 to get:
y=2x-5 then sub it into the 1st equation then sovle it? Thats what im guessing you should do
3. (Original post by AnnaClara)
x^2 + y^2 = 25
2x - y = 5

And

x^2 + 2xy + 15 = 0
2x - y + 10 =0

I could do all the others on the worksheet but I've checked the answers for these two and still don't understand how to do them
when you are doing simult. equations with a linear and a quadratic you want to use substitution, re-arrange the linear equation to get either x or y on its own (its up to you but getting y on its own is easier). Then substitute this into the quadratic equation, replacing every "y" you see with "2x - 5", then solve for x from there, finally sub into the linear to find value(s) for y.

same method for the second one
4. (Original post by AnnaClara)
x^2 + y^2 = 25
2x - y = 5

And

x^2 + 2xy + 15 = 0
2x - y + 10 =0

I could do all the others on the worksheet but I've checked the answers for these two and still don't understand how to do them
Rearrange for y within the linear equations. You can use this to substitute these expressions into the equations above. By doing so you are making the y coordinates equal for both the curve and the line where the two intersect then proceeding to find the x coordinates by simply solving the quadratics in terms of x.

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