Solve Equation Numerically

In mathematics, to solve an equation is to find what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an equation (two expressions related by equality). These expressions contain one or more unknowns, which are free variables for which values are sought that cause the condition to be fulfilled. To be precise, what are sought are often not necessarily actual values, but, more in general, mathematical expressions (Source from Wikipedia). Here are going to solve equation numerically and its examples.

Solving equation numerically - Example problems:

Solve equation numerically - Example: 1

To solve the following equation,

2x+3+3x =8

Solution:

Add the like terms

Here the like terms is 2x and 3x

2x+3x=5x

Therefore the equation is

5x+3=8

Add both sides -3

5x+3-3 =8-3

5x=5

Divide both sides 5

There fore the value of x=1

Solve equation numerically -  Example: 2

Solve the following equation by substitution method

x-y =3

2x+4=6

Solution:

x-y =3…………….1

2x+4=6……………2

From the equation 1 can we write

x=y+3……………..3

Substitute x value in equation 1

Therefore

2x+4=6

2(y+3) =6

2y+6=6

Add both sides -6

2y+6-6=6-6

2y=0

y=0

Substitute y=0 in equation 3

x=y+3

x=0+3

x=3

Therefore the solution is x=3, y=0

Solve equation numerically - Example:3

To solve the following expression,

5x+3 = 2x+1

Move the 3 to the right hand side by subtracting 3 from both sides, like this:

From the left hand side:
3 - 3 = 0

The answer is 5x

From the right hand side:
1 - 3 = -2

The answer is -2+2x

Now, the equation reads:

5x = -2+2x

Move the 2x to the left hand side by subtracting 2x from both sides, like this:

From the left hand side:

5x - 2x = 3x

The answer is 3x

From the right hand side:

2x - 2x = 0

The answer is -2

Now, the equation reads:

3x = -2

To isolate the x, we have to divide both sides of the equation by the other variables around the x on the left side of the equation.

The solution to your equation is:

x =-2/3