All about simulitious equations

On occasions you will come across two or more unknown quantities, and two or more equations

relating them. These are called simultaneous equations and when asked to solve them you

must find values of the unknowns which satisfy all the given equations at the same time.

Step-by-step explanation:

1. The solution of a pair of simultaneous equations

The solution of the pair of simultaneous equations

3x + 2y = 36, and 5x + 4y = 64

is x = 8 and y = 6. This is easily verified by substituting these values into the left-hand sides

to obtain the values on the right. So x = 8, y = 6 satisfy the simultaneous equations.

2. Solving a pair of simultaneous equations

There are many ways of solving simultaneous equations. Perhaps the simplest way is elimination. This is a process which involves removing or eliminating one of the unknowns to leave a

single equation which involves the other unknown. The method is best illustrated by example.

Example

Solve the simultaneous equations 3x + 2y = 36 (1)

5x + 4y = 64 (2) .

Solution

Notice that if we multiply both sides of the first equation by 2 we obtain an equivalent equation

6x + 4y = 72 (3)

Now, if equation (2) is subtracted from equation (3) the terms involving y will be eliminated:

6x + 4y = 72 − (3)

5x + 4y = 64 (2)

x + 0y = 8

step-by-step explanation:

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.