Smoky saif
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how would you work out a question like this

given that: x+y = 5 and that (x+4)(y+4) = 55

find the value of xy
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Charlie101998
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I'd start by expanding the brackets in the second equation. The in the first say x = 5 - y. You can then use that in the second equation to work out the value of y. Using that Value of y, find x in the first equation and check to make sure it works in the second.
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Smoky saif
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(Original post by Charlie101998)
I'd start by expanding the brackets in the second equation. The in the first say x = 5 - y. You can then use that in the second equation to work out the value of y. Using that Value of y, find x in the first equation and check to make sure it works in the second.
okay but I get -y^2 +5y -19. Is that solvable?
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DFranklin
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(Original post by Charlie101998)
I'd start by expanding the brackets in the second equation. The in the first say x = 5 - y. You can then use that in the second equation to work out the value of y. Using that Value of y, find x in the first equation and check to make sure it works in the second.
In this case, you can expand, and then directly use what you know to get an expression for xy. There should be very little calculation involved.
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Nour M.
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There are two ways of solving this question, with one more complex than the other.

1) Long method involves solving directly for either x or y, then using the value obtained to calculate the other variable, before finally multiplying both values together to find the value of xy. You can use the method of the simultaneous equation for this but as you have probably figured out on your own that that would result in a series of complicated equations. In a previous reply, you said you'd get one equation such as: -y^2 + 5y -19, which is in fact solvable but unfortunately has no real number solutions. However, all of this can be avoided by using the next method.

2) Direct substitution and solving. Since they didn't ask for the exact value of either x or y, I'd suggest you should start looking for ways to directly solve for the expression of xy from what you know. Try to break apart what you've been given and play around with the terms and relate both equations with each other.

Edited for paragraphing
Last edited by Nour M.; 3 weeks ago
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DFranklin
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(Original post by Nour M.)
~snip~
I can see you've put in a lot of effort, but there's a rule against posting full solutions: https://www.thestudentroom.co.uk/sho...8#post73536820
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Nour M.
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(Original post by DFranklin)
I can see you've put in a lot of effort, but there's a rule against posting full solutions: https://www.thestudentroom.co.uk/sho...8#post73536820
Oh, my bad, I wasn't aware of this rule at the time. I'll edit my reply to the question to make it more accomodating to the rule. Thank you!
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Smoky saif
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(Original post by Nour M.)
Oh, my bad, I wasn't aware of this rule at the time. I'll edit my reply to the question to make it more accomodating to the rule. Thank you!
Also thank you for showing me how to do it. I never got to thank you. I appreciate it.
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