equations tricks

To solve some equations visually:

If the equation contains a common term on both sides then the term is equal to zero. E.g. . . 5y-8y= 7y+9y Since -3 cannot be equal to 16 hence y has to be equal to 0.

Let us take another example,
4(1+x) – 5(1+x) = 9(1+x) + 6(1+x)
Since 4-5 is not equal to 9+6 hence (1+x) =0

How to solve an equation with two fractions with the same numerator:

If we have an equation containing two fractions with the same numerator then we can solve them by adding the denominators to get the value of the unknown term.
For example,
If we have the following equation,
1/ (3+2x) +1/ (9x) =0
Then we can solve it by adding the denominators
3-2x +9x=0
7x=3
x=3/7

Let us try another example
1/ (4z-9) -1/ (5z+7)=0
Hence 4z-9+5z-7=0
9z-2=0
9z=2
z=2/9

The key to solving simultaneous simple equations:

If the coefficients of one of the terms are in a specific ratio then we can safely assume that the value of the other constant is going to be zero.

For example Let us consider the following two equations
3000a+6000b=4000
9000a+5000b=12000
As we can see the coefficients for A are in the ratio of 1:3 and the independent terms that they are equated to are also in the same ratio. Hence if we equate b with zero it will be easier to solve for a.
Therefore we get 3000a=4000 and 9000a=12000, under both circumstances the value for a remains the same i.e. a= 4/3

Let us try it with another set of equations
7000x-800y=3000
900x-400y=1500
In this case we can see that the coefficients of y and the independent terms are both in the ratio of 2:1 and therefore we can safely equate the x term with zero. Hence solving for y in both cases we will get
-800y=3000 and -400y =1500
Hence y = -15/4

This method can also be used to solve a couple of simultaneous quadratic equations easily.