Math Is Fun Forum
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#1 2014-03-28 04:04:31
- PatternMan
- Member
- Registered: 2014-03-08
- Posts: 199
Can you think of any different ways to solve this?
The value of (x - 4)(y + 3) is - 10
Work out the possible pairs of values for x and y
I looked at this and couldn't think of any procedure to solve this but it says the two brackets = -10 so you got to make them multiply to make - 10. So I just used some trial and error method so I have to make them both = 10. 10 has factors of 1 and 10, 2 and 5. How many different ways can I make 1,2, 10, and 5 in each bracket.
For x
5 -4 = 1
3 -4 = -1
6 -4 = 2
2 - 4 = -2
9 - 4 = 5
14 - 4 = 10
-6 - 4 = - 10
So I can tell there's 7 different ways. The I just match the y with the other factor
for y
-13 + 3 = 10 so when x = 5, y = -13 and so on
7 + 3 = 10
-8 + 3 = -5
Last edited by PatternMan (2014-03-28 04:05:37)
"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."
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#2 2014-03-28 04:15:06
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
Hi;
Looks like there are 8 answers.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2014-03-28 04:49:21
- PatternMan
- Member
- Registered: 2014-03-08
- Posts: 199
Re: Can you think of any different ways to solve this?
Hi;
Looks like there are 8 answers.
What's the last answer? oh - 5
x = -1 and y = -1
Last edited by PatternMan (2014-03-28 04:51:29)
"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."
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#4 2014-03-28 04:54:09
Re: Can you think of any different ways to solve this?
How about x = 6.5, y = 7. There are infinite answers
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#5 2014-03-28 05:00:11
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
Yep, the first rule. Put down the constraints. x,y = Integers will do fine.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#6 2014-03-28 05:08:19
- PatternMan
- Member
- Registered: 2014-03-08
- Posts: 199
Re: Can you think of any different ways to solve this?
Yep, the first rule. Put down the constraints. x,y = Integers will do fine.
The question never stated whether they only wanted integer solutions or not. However since it's for my level I assume that's what they wanted. This is a reason why I don't like a lot of exam questions I come across. The question is not well defined and you have to think within their constraints to give the correct answer. Even if they constraints are not well defined.
"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."
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#7 2014-03-28 05:12:24
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
I assumed you wanted integers too.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#8 2014-03-28 05:31:58
Re: Can you think of any different ways to solve this?
It is a hyperbole. Why do you want to assume that only integer solutions are desired?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#9 2014-03-28 05:35:41
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
I did not want to assume it for any special reason. I looked at his 7 solutions. They are all integers, so I was just pointing out that there are 8 integer solutions.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2014-03-28 05:40:19
Re: Can you think of any different ways to solve this?
Work out the possible pairs of values for x and y
Given that question I would solve for y and tell that for every value of x, there is a y which makes the equation true and hence there are infinite solutions. That atleast, would take less time for writing down.
However since it's for my level I assume that's what they wanted.
What level is he talking of?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#11 2014-03-28 05:41:43
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
He like me must love the integers best. Do you know why?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#12 2014-03-28 05:44:20
Re: Can you think of any different ways to solve this?
yes.
God created Integers.
I love integers the best but you love fractions more.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#13 2014-03-28 05:46:07
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
Fractions are just integers over integers. I will have to ask God whether he specifically made the integers. It could have been an incredibly clever reppie.
But that is not the reason I love the integers.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2014-03-28 05:47:49
Re: Can you think of any different ways to solve this?
Why is God an incredibly clever reppie? Is he not a bumpkin?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#15 2014-03-28 05:49:29
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
No, he is not a reppie. I am just saying that it might have been given to man by a reppie.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#16 2014-03-28 05:53:12
Re: Can you think of any different ways to solve this?
A bumpkin, he is, hmm?
Integers, the next likes, no approximation error it has, thus.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#17 2014-03-28 05:57:12
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
Exact a Mundo! No error! I am a numerical analyst first. We study error.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#18 2014-03-28 05:59:34
Re: Can you think of any different ways to solve this?
Chaos Theorist, are you not, hmm?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#19 2014-03-28 06:00:55
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
Chaos is kaboobly doo.[comment removed]
But back to the topic of the the thread.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#20 2014-03-28 06:19:29
- PatternMan
- Member
- Registered: 2014-03-08
- Posts: 199
Re: Can you think of any different ways to solve this?
Work out the possible pairs of values for x and y
Given that question I would solve for y and tell that for every value of x, there is a y which makes the equation true and hence there are infinite solutions. That atleast, would take less time for writing down.
However since it's for my level I assume that's what they wanted.
What level is he talking of?
This is a GCSE syllabus question for 15-16 year olds usually which is taken at the end of school here in the UK. They don't covere parabolas at that level. They just touch on reciprocal graphs. Also this question was on the first or second page and not at the back and they don't require you to understand that much.
"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."
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#21 2014-03-28 21:05:20
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,621
Re: Can you think of any different ways to solve this?
hi PatternMan,
This is a GCSE syllabus question
Really! Where did it occur? In the sample paper? I'm surprised that they 'forgot' to specify integers. What exam board would leave that out?
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#22 2014-03-29 03:29:17
- Ronaphy Olga
- Member
- Registered: 2014-03-13
- Posts: 4
Re: Can you think of any different ways to solve this?
can someone help me with this:
(3^2 2^-1 - 2^-4 3^-5)^-2.
give the answer as fractions.
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#23 2014-03-29 03:33:28
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
Re: Can you think of any different ways to solve this?
Ronaphy Olga, what operation is between the terms in the brackets?
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#24 2014-03-29 03:36:00
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Can you think of any different ways to solve this?
Hi Ronaphy Olga;
Please use latex for math and start a new thread next time for new questions.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#25 2014-03-29 03:38:49
- Ronaphy Olga
- Member
- Registered: 2014-03-13
- Posts: 4
Re: Can you think of any different ways to solve this?
i think its multiplication
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