simultaenous equations??

guest3 · 2007-12-01 01:00:18

can anyone please help me, how to work out: 3x-4y=4.5
2x+2y=10

thank you

luca-deltodesco · 2007-12-01 01:06:11

theres always two methods of doing these sort of things (Well 3 really, but lets stick to 2)

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first is to manipulate one or both equations so that they share a common coeffecient. for example here we could do:

3x-4y=4.5 -> 6x-8y=9
2x+2y=10 -> 6x+6y=30

and then you can subtract them to get:

14y=21
y = 1.5

then use that in one of the equations to get x, lets choose
2x+2y=10 -> 2x+3=10, 2x = 7, x = 3.5

which gives : x = 3.5, y = 1.5

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the second way is to manipulate one of the equations to get an equation for y in terms of x, or x in terms of y, and substitute this into the other equation, for example:

3x-4y=4.5
2x+2y=10:

2x=10-2y, x = 5-y

3(5-y)-4y=4.5
15-3y-4y=4.5
15-4.5=7y
7y = 10.5
y = 1.5, x = 5-y = 3.5

x = 3.5, y = 1.5

i personally prefer to use the second method as it means only doing one substitution

JohnnyReinB · 2007-12-01 16:36:50

What's the third way?

luca-deltodesco · 2007-12-01 21:29:58

Third way: The simulataneous equaitons can be written as a single equation

Last edited by luca-deltodesco (2007-12-01 21:31:19)

mathsyperson · 2007-12-02 00:57:53

4th way: Draw both curves on a graph and see where they intersect. Only works if the answers are integers though (or at least a fairly simple fraction).

Math Is Fun Forum

#1 2007-12-01 01:00:18

simultaenous equations??

#2 2007-12-01 01:06:11

Re: simultaenous equations??

#3 2007-12-01 16:36:50

Re: simultaenous equations??

#4 2007-12-01 21:29:58

Re: simultaenous equations??

#5 2007-12-02 00:57:53

Re: simultaenous equations??

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