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simultaneous equations HELP!!

Does anyone know an easy way to do simultaneous equations? I've tried everything and just can't seem to get it right!

thanks:smile:
Reply 1
Rearrange one equation to make it x= or y= and then just sub it into the other equation. One of the unknowns won't be there, when you have the answer for one sub it back into a equation for the other unknown.
If you post an example question, or one you're specifically stuck on, we'd be able to put the method into context so you'd understand easier :biggrin:

But yes, as chloe_32 stated, I would rearrange either equation 1 or 2 and substitute it into the other.

For example;

If we have

Equation 1: 3x+5y24=03x+5y-24=0 and
Equation 2: 5x+8y+36=05x+8y+36=0

If we take Equation 1 and rearrange for x x we get:

3x=245y 3x=24-5y

\Rightarrow x=245y3 x = \dfrac{24-5y}{3}

Now if we substitute this into Equation 2

5(245y)3+8y+36=0 \dfrac{5(24-5y)}{3}+8y+36=0

Now we can solve Equation 2 for y y

You would get 12025y3+8y+36=0 \dfrac{120-25y}{3}+8y+36=0

12025y+24y+108=0 120-25y+24y+108 =0

\Rightarrow y=228 y=228

Now, let's substitute this yy value into equation 1 to get the x x value.

y=228 y=228

3x+5y24=0 3x+5y-24=0

3x+5(228)24=0 3x + 5(228)-24=0

\Rightarrow x=372 x= -372

Therefore you have x=372 x= -372 and y=228 y=228

Hope this helps :biggrin:


P.S. I made the question up on the spot, don't be thrown off by the answers, concentrate on the method instead :biggrin:
(edited 8 years ago)
Reply 3
Original post by chloe_32
Rearrange one equation to make it x= or y= and then just sub it into the other equation. One of the unknowns won't be there, when you have the answer for one sub it back into a equation for the other unknown.

Thank you!!
Reply 4
Original post by edothero
If you post an example question, or one you're specifically stuck on, we'd be able to put the method into context so you'd understand easier :biggrin:

But yes, as chloe_32 stated, I would rearrange either equation 1 or 2 and substitute it into the other.

For example;

If we have

Equation 1: 3x+5y24=03x+5y-24=0 and
Equation 2: 5x+8y+36=05x+8y+36=0

If we take Equation 1 and rearrange for x x we get:

3x=245y 3x=24-5y

\Rightarrow x=245y3 x = \dfrac{24-5y}{3}

Now if we substitute this into Equation 2

5(245y)3+8y+36=0 \dfrac{5(24-5y)}{3}+8y+36=0

Now we can solve Equation 2 for y y

You would get 12025y3+8y+36=0 \dfrac{120-25y}{3}+8y+36=0

12025y+24y+108=0 120-25y+24y+108 =0

\Rightarrow y=228 y=228

Now, let's substitute this yy value into equation 1 to get the x x value.

y=228 y=228

3x+5y24=0 3x+5y-24=0

3x+5(228)24=0 3x + 5(228)-24=0

\Rightarrow x=372 x= -372

Therefore you have x=372 x= -372 and y=228 y=228

Hope this helps :biggrin:


P.S. I made the question up on the spot, don't be thrown off by the answers, concentrate on the method instead :biggrin:


Thank you so much!! In regards to the specific example how would you work out:

4x + 6y = 12
x + y = 1
Original post by libertyd
Thank you so much!! In regards to the specific example how would you work out:

4x + 6y = 12
x + y = 1


Y=1-x
Substitute

Posted from TSR Mobile
Original post by libertyd
Thank you so much!! In regards to the specific example how would you work out:

4x + 6y = 12
x + y = 1


Well here we have a simple choice don't we.

You can start by rearranging equation 2 to get

x=1y x = 1-y
or
y=1x y= 1-x

To make it easier for yourself, always go for the simplest equation. No matter which equation you rearrange, the outcome will be the same.

Try it :biggrin:
(edited 8 years ago)
Original post by libertyd
Thank you so much!! In regards to the specific example how would you work out:

4x + 6y = 12
x + y = 1


So you would rearrange the second to be x=1-y or y=1-x its your choice.

Then sub it in

y=1-x
4x + 6(1-x) =12
And work from there

work out your X, then sub into original equation to get y

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