Introduction of Simultaneous Equations

Let us study about Simultaneous Equations,


Simultaneous Equations :
If you have two equations with the same two unknowns in each, you can solve for both unknowns. There are three common methods for solving: addition/subtraction, substitution, and graphing.


Addition/subtraction method :

To use the addition/subtraction method,

1. Multiply one or both equations by some number to make the number in front of one of the letters (unknowns) the same in each equation.

2. Add or subtract the two equations to eliminate one letter.

3. Solve for the other unknown.

4. Insert the value of the first unknown in one of the original equations to solve for the second unknown.

Example : Solve for x and y.
First multiply the bottom equation by 3. Now the y is preceded by a 3 in each equation.
Now the equations can be subtracted, eliminating the y terms.
Now insert x = 5 in one of the original equations to solve for y.
Answer: x = 5, y = 3

Of course, if the number in front of a letter is already the same in each equation, you do not have to change either equation. Simply add or subtract.
I hope the above explanation was useful.