Simultaneous Equations (Linear)
Recreated 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
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