N equations simultaneously solved for N unknown variables

Simultaneous equations may be solved by

Addition Method

1. Multiply one equation by a suitable number
2. Add that equation to other equation(s)
3. Eliminate one variable
4. Solve for the remaining variable(s)

Example

Solve the following simultaneous equations by the addition method

Substitution Method

1. Solve for one variable as a function of other variable(s)
2. Substitute the variable in other equation(s), thus eliminating it
3. Solve for the remaining variable(s)

Example

{	x+y=3 3x-2y=14

 

Solve the first equation for x

x=3-y

Substitute x in second equation, solve for y

9-3y-2y=14 Þ -5y=5 Þ y=-1

Solve for x by substituting y in the first equation

x-1=3 Þ x=4

{	2x-3y+5=0 3x+2y=12

 

 

 

 

 

 

{	-2x+y=0.1 3x+5y=-4.7

{	x+y=3 3x-2y=14