Simultaneous equations

Hi

,

I need help trying to explain what is going on with solving a set of simultaneous equations.

I know how to solve them, I just do not know how to talk about them in a more technical sense.

For example:

2x + 4y = -26
6x + 8y = -36

What I do is multiply the equation(s) (if needed), to get either the x or y terms to be the same. (How can I do this? Like, what is the mathematical law stating that by multiplying them, allows them to still give the same result?)

Then onto adding or subtracting these two new equations to leave either the x or y term.

Solve for x or y then substitute this back in to get the other variable.

Hope that makes sense as I am basically trying to talk about how to solve simultaneous equations to someone who knows about maths on a technical level

Thanks

Hmmm......

12x+24y=-156
12x+18y=-72
+24y-18y=156-72=84

6y=84/6=14
...............

(edited 9 years ago)

Original post by jojo55

Like, what is the mathematical law stating that by multiplying them, allows them to still give the same result?)

This might help.

Reply 4

Anon74

2x + 4y = -26

6x + 8y = -36

What I do is multiply the equation(s) (if needed), to get either the x or y terms to be the same. (How can I do this? Like, what is the mathematical law stating that by multiplying them, allows them to still give the same result?)
The mathematical law is that if you have to sides of an equation which are the same (represented by the =), you can do anything to both of the sides and they will remain the same, for example , 5 + 3 = 8 and, 5(5 x 3) = 5 x 8.

Now, lets say you multiplied the top equation by 2, going from 2x +4y= -26 to 4x + 8y= -52. Now you have the same number of y's in each equation so you do:
4x + 8y = -52
6x + 8y = -36 (just simply subtract the bottom one from the top one giving)
-2x + 0y = -16 therefore -2x = -16 meaning 2x = 16 and x = 8

Now that you have your x value you can substitute the value of x back into the original equations and see if they both match up.

2x + 4y = -26 x = 8 ----> 2(8) + 4y = -26 --> 16 +4y = -26 --> 4y = -42 --> y = -10.5

6x + 8y = -36 x = 8 ----> 6(8) + 8y = -36 --> 48 +8y = -36 --> 8y = -84 --> y = -10.5

If they don't match you've made a mistake somewhere

(edited 9 years ago)

Reply 5

German123

21

Original post by jojo55

Hi

,

I need help trying to explain what is going on with solving a set of simultaneous equations.

I know how to solve them, I just do not know how to talk about them in a more technical sense.

For example:

2x + 4y = -26
6x + 8y = -36

What I do is multiply the equation(s) (if needed), to get either the x or y terms to be the same. (How can I do this? Like, what is the mathematical law stating that by multiplying them, allows them to still give the same result?)

Then onto adding or subtracting these two new equations to leave either the x or y term.

Solve for x or y then substitute this back in to get the other variable.

Hope that makes sense as I am basically trying to talk about how to solve simultaneous equations to someone who knows about maths on a technical level

Thanks

I dont really know how to explain but i can sort of do it as this(not exactly the same question) came up on my final GCSE maths exm....dont really know whether my working out is correct as it was long time ago since i did these hahaha. :smile:

Reply 6

MathMeister

10

I don't see a better way of seeing why you can do this other than algebraically. You can solve the linear equations because they intersect. If you multiply one of the equations, lets say by 3 so you can then eliminate one, you can do this because the resultant equation is the same.
I.e x+2y=3 is the same as 2x+4y=6 so then you could eliminate lets say 2x+3y=4 (because you are taking the same from both sides )
Are you sure there is a technical way of understanding such a simple idea? Surely one is not needed...

(edited 9 years ago)

Reply 7

davros

16

Original post by jojo55

Hi

,

I need help trying to explain what is going on with solving a set of simultaneous equations.

I know how to solve them, I just do not know how to talk about them in a more technical sense.

For example:

2x + 4y = -26
6x + 8y = -36

What I do is multiply the equation(s) (if needed), to get either the x or y terms to be the same. (How can I do this? Like, what is the mathematical law stating that by multiplying them, allows them to still give the same result?)

Then onto adding or subtracting these two new equations to leave either the x or y term.

Solve for x or y then substitute this back in to get the other variable.

Hope that makes sense as I am basically trying to talk about how to solve simultaneous equations to someone who knows about maths on a technical level

Thanks

You're basically relying on one of the axioms of mathematics that says that if
a = b
then
ca = cb

and then doing manipulation with the consequences of that.

Alternatively, you can rearrange each equation so that it's in the form:
x = something
and
x = something else

and then use the axiom that if a = b and a = c then b = c

Simultaneous equations

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