o level maths question

[kopend]

11) Solve the simultaneous equations:
3x - 4y = 25
4x - 5y = 32

x =
y =

[squarebear]

You are correct. -4 take away another 4 is -8

[ladyalex]

OMG....even squarebear agrees with me.....faints with astonishment......

[squarebear]

lol

[Old_Geezer]

The 'brute force' method of trying every number in turn works eventually, but you don't get through enough questions in the exam time available that way. Always better to understand how to do sonmething & why it works.

[ladyalex]

Well, after my first blunder on this thread.....

[flip_flop]

Jesus Christ, the horror of double maths with Mr Weitzal on a Wednesday afternoon has just come screaming back to me.

Didn't understand it then and sure as hell don't now!

[Old_Geezer]

The general rule is to multiply one equation by whatever it needs so that it either has the same number of x as the other equation, or the same number of y.

Once you have done that you can subtract the other original equation from the one you just calculated, to get an equation with just a single unknown variable, which is trivial to solve.

Having worked out one variable you just substitue for it in one of the equations and solving for the other unknown becomes trivial.

[mike11111]

If I remember correctly that is one method (the easier) called elimination. We were taught how to do that after we had mastered the harder method, called substitution, whereby in one of the equations y would be expressed in terms of x then substituted into the other equation.

[Old_Geezer]

I try not to do things the hard way if there is an easier option ;-)

IIRC one can also change the problem into a matrix one, but my school days are too far in the past to recall that solution.

[mike11111]

We were always taught to do things the hard way first, before learning the easier way, for sound educational reasons.

[dr b]

Conceptually it's a little harder to see why it works, but mathematically it's always easier to use Cramer's rule (method of determinants) to solve these:

http://en.wikipedia.org/wiki/Cramer%27s_Rule

x = [(25)(-5)-(32)(-4)] / [(3)(-5) - (4)(-4)] = 3

y = [(3)(32)-(4)(25)] / [(3)(-5) - (4)(-4)] = -4

[ladyalex]

I'm sure you are right, dr b, but I'll stick to my way, even if I sometimes slip up with the plus and minus signs.

[karimjee52]

x= 3
y= -4

[Shaqeeq]

3x-4y=25 - Equation 1
4x-5y=32 - Equation 2
Equation 1*4
Equation 2*3
4(3x-4y=25) - Equation 3
3(4x-5y=32) - Equation 4
12x-16y=100
12x-15y=96
therefore equation 3-equation 4
y=4
substitute equation y=4 in equation 2
4x-(5*4)=32
4x=32-20
then x=12

[avikesh]

x= 3 and y= -4