3x+4y = 24
4x+3y = 22
Thanks, Would be helpful if you can break it down
How do I do this Simultaneous Equation
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 07092016 23:24

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 07092016 23:27
(Original post by DabSchool)
3x+4y = 24
4x+3y = 22
Thanks, Would be helpful if you can break it down 
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 07092016 23:28
(Original post by DabSchool)
3x+4y = 24
4x+3y = 22
Thanks, Would be helpful if you can break it down
What could we multiply the first and second equation by so that the number in front of the x is the same? 
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 07092016 23:29
(Original post by DabSchool)
3x+4y = 24
4x+3y = 22
Thanks, Would be helpful if you can break it downPost rating:2 
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 07092016 23:36
the x's and the y's must equal each other out. to make it easier do first the x's and then the y's. therefore you need to multiply the upper equation with 4 and the lower equation with 3 to make the x's equal to 0 therefore:
4(3x+4y=24)3(4x+3y=22)you need to multiply both equations therefore : 12x+16y= 96
12x9y=66now : 12x12x=0 therefore you solve for y :16y9y=7y and 9666= 30 your equation should look like this : 0x + 7y = 30 7y=30 y= 4.23
And then you solve for x (by putting where y is 4.23) : 12x + 16(4.23) = 96
12x + 67.68 = 96
12x = 28.32
x= 2.36 
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 07092016 23:45
(Original post by DabSchool)
3x+4y = 24
4x+3y = 22
Thanks, Would be helpful if you can break it downSpoiler:ShowEqual the X or Y; I've chosen X
12x + 16y = 9612x + 9y = 66
Put the Xs to one side
12x = 96  16y
12x = 66  9y
Put the equations together
96  16y = 66  9y
Work it through to find Y
96 = 66 + 7y
7y = 30y = 4.3
Put Y into the original equation
3x + 17.2 = 24
3x = 6.8
x = 2.3Last edited by Ezme39; 08092016 at 12:54. 
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 07092016 23:46
Thank you (and everyone else). Few questions...
1) Can you work with X and Y to get it the same ?
2) Do you have to write 30 over 7 and why 
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 08092016 00:01
(Original post by DabSchool)
Thank you (and everyone else). Few questions...
1) Can you work with X and Y to get it the same ?
2) Do you have to write 30 over 7 and why
2) Yes because it's an exact solution. Better get comfortable with fractions fast. 
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 08092016 00:03
(Original post by Ezme39)
Haven't done these in years, so having a go for fun very rough as it's without a calculator... seems close though looking at other peoples answers
Equal the X or Y; I've chosen X
12x + 16y = 96
12x + 9y = 66
Put the Xs to one side
12x = 96  16y
12x = 66  9y
Put the equations together
96  16y = 66  9y
Work it through to find Y
96 = 66 + 7y
7y = 30
y = 4.3
Put Y into the original equation
3x + 17.2 = 24
3x = 6.8
x = 2.3
(Original post by Evita Tzn)
the x's and the y's must equal each other out. to make it easier do first the x's and then the y's. therefore you need to multiply the upper equation with 4 and the lower equation with 3 to make the x's equal to 0 therefore:4(3x+4y=24)3(4x+3y=22)you need to multiply both equations therefore : 12x+16y= 9612x9y=66now : 12x12x=0 therefore you solve for y :16y9y=7y and 9666= 30 your equation should look like this : 0x + 7y = 30 7y=30 y= 4.23And then you solve for x (by putting where y is 4.23) : 12x + 16(4.23) = 9612x + 67.68 = 9612x = 28.32x= 2.36Last edited by RDKGames; 08092016 at 00:07. 
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 08092016 00:42
(Original post by RDKGames)
Good attempt, but you rounded your answers so your solutions are technically wrong. 
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 08092016 01:09
(Original post by Ezme39)
Yeah, I just didn't have a calculator on me, so did rough mental maths instead 
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 08092016 07:41
(Original post by B_9710)
It's easier to give an answer as 30/7 without a calculator than as a decimal, no? 
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 08092016 11:09
(Original post by Ezme39)
Not to then put it in the equation, imo but with a calculator of course you could just keep the number in there, and proceed with the next calculation 
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 08092016 12:55
(Original post by B_9710)
Even so it's surely easier to multiply fractions than decimals? 
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 08092016 13:06
Whenever you see a simultaneous equation you should think of overlapping curves or surfaces. If your equation has two variables (x, y) then it is a curve, if it has three variables it is a surface, if it has n it is an (n1)  dimensional manifold. Why the 1? Well that's because one of the variables is determined by the equation, so in the case of a line x + 2y = 0, a given x completely determines y.
It is important to notice that I can multiply this equation by any number to produce the same line, e.g. x + 2y = 2x + 4y = 10x + 20y = 0 etc. Any other linear equation will produce a different line.
If you just work with just one of the equations you will never find numerical values for x or y unless it is a horizontal or vertical line. That is because there are an infinite number of solutions (x,y) to a line.
If you are hoping to twiddle 3x + 4y = 24 around to get 4x + 3y = blah, I'm afraid that cannot ever happen. The first equation should be thought of as an assumption/assertion that "this line exists.". It should be obvious intuitively that the second equation, equivalent to the assertion that "this other line also exists.", does not follow logically. A single line existing by itself is perfectly fine, so the existence of a second equation is an assumption plucked out of thin air. You could choose to have more lines if you wanted.
Algebraic twiddling is equivalent to a pure logical argument; which is to say it does not change the properties of the line e.g. 3x + 4y = 24 is the same line as 3x  4y = 24.
What is special is that we are using (x,y) in both equations, so implicitly we have the added assumption that "there exists a point (x,y) on both lines." Such a point does not always exist; for example if the second equation were 3x + 4y = 25 the second line would be parallel and offset. If there are more than 2 equations of a line in 2D space, it might also fail.
To attempt to find a solution, you simply need to combine the two (or more) equations into a single equation. It really does not matter how you do this, provided you don't stray from the laws of algebra. A common way is to manipulate the variables in both equations independently until you get A = blah and B = blah, then take A = B and solve for x or y. This may not be numerical, but if you substitute your solution for into either of the equations you are certain to obtain a numerical solution.
The problem of solving simultaneous linear equations is extremely important in every technical field and it is right at the heart of quantum mechanics. We call it linear algebra and usually use matrix representations, which are grids of numbers or variables. With this approach you can solve such equations very easily, although the algorithm seems weird until you get a bit deeper into the maths.Last edited by alephu5; 14092016 at 17:21. Reason: Not good formatting 
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 08092016 13:17
(Original post by alephu5)
Whenever you see a simultaneous equation you should think of overlapping curves or surfaces. If your equation has two variables (x, y) then it is a curve, if it has three variables it is a surface, if it has n it is an (n1)  dimensional manifold. Why the 1? Well that's because one of the variables is determined by the equation, so in the case of a line x + 2y = 0, a given x completely determines y...Last edited by notnek; 08092016 at 13:20.Post rating:1 
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 08092016 13:29
The OP asked
1) Can you work with X and Y to get it the same ? 
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 08092016 13:38
(Original post by #engineer)

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 08092016 13:46
(Original post by ubi1)
Is this Gcse maths Grade C question? 
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 08092016 13:55
Not very clear but I've attached a guide to solving this equation:
HTH
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Updated: September 8, 2016
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