# Simultanous equations

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**Simultaneous Equations (Linear)**

*R**ecreated from a Revision Book. One presumes there is no copyright on Maths*

1. Let us assume that you are asked to solve the following pair of equations

2x = 6 - 4y

-3 - 3y = 4x

We must rearrange both equations such that

ax + by = c

*where a,b, and c are numbers*

Thus

2. 2x + 4y = 6

-4x -3y =3

*(rember you are potentialy swapping numbers from both sides of the equation, so they may become negative and vice versa)*

Be sure to label those kwrazy equations!

2x + 4y = 6 (1)

-4x -3y =3 (2)

3. You must 'match' the coefficents of *either* the X's OR Y 's in both equations . This is done by multiplying either one or both of the equations by a suitable number. A postive may match a negative (its far less problematic than rhesus's anyway)

Therfore if we multiply

2x + 4y = 6 (1)

by 2 we should thus get

4x + 8y = 12 (1)

and you'll notice the 4 of the coefficent of X matches

-4x -3y =3 (2)

(Negative no problem)

Be sure to renumber those kwrazy equations !

4x + 8y = 12 (3)

-4x -3y =3 (4)

3. If the Coefficents are the same (both +ve or both -ve) then **SUBTRACT**

If the Coefficents are different (one +ve and one -ve) then **ADD**

The latter rule applies here and thus

(3) + (4) 0x +5y =15

Solve this remaining equation

5y =15 - - > y= 3

4. Now subsitue this value back into equation (1)

2x + 4 x 3 = 6 - - > 2x + 12 = 6 - - > 2x = -6 - - > x = -3

5. Now subsitute both equations back into equation (2) and it should work . If not

(*Na just try again or ask someone else*)

(-4 x -3) -( 3 x 3) = 3

x = -3 , y = 3

Re-edited for clearing confusion.Danke Phantasm

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