Math Related Articles

Introduction to math related articles:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.(Source: From Wikipedia). Now, we are going to discuss about the following math related articles:

1) Simultaneous equations article and

2) General slope form article.


Some math related articles explanation:


Simultaneous equations article:

In algebra, the simplest technique of linear system involves two equations and two variables:

3x+3y=6

4x+2y=5

Here, x and y are the two variables. Generally, a letter is used to denote the variable in the expression or equation.

The following methods are used to solve the simultaneous equations:

1) Substitution method

2) Elimination method

3) Matrix method

4) Graphing method.

Article on general slope form:

The slope (m) of a line in the plane containing the x and y axes is generally represented as

m = Δy / Δx

Δy = y2-y1

Δx = x2-x1

When the two points (x1, y1) and (x2, y2) are known, then the general formula to find the slope, m = (y2-y1) / (x2-x1)

Slope Intercept Form is used to create the straight line equation with a y-intercept (b) and slope m of the line.

General slope Intercept Form:  y = m x + b

b = y-intercept of the line,

m = Slope of the line.

The graph of this equation is a straight line.

I have recently faced lot of problem while learning List Odd Numbers, But thank to online resources of math which helped me to learn myself easily on net.

Worked math related articles examples:


Example problem related to Simultaneous equations:

Solve the simultaneous equations by substitution method:

x + y = 20 -------equation (1)
3x + 11y = 100 ------equation (2)

Step 1: From equation (1)

x + y = 20

Subtract x on both sides of the equation

x + y –x = 20 –x

y = -x +20------------------Equation (3)

Substitute the equation (3) in equation (2)

3x + 11y = 100

3x + 11(-x +20)=100

3x -11x +220=100

-8x +220=100

Subtract 220 on both sides of the equation

-8x +220 -220=100 – 220

-8x=-120

Divide by -8 on both sides of the equation

-8x/-8=-120/-8

x = 15

Step 2: Substitute the value x in equation (1)

x + y = 20

15+y=20

y=5

So, the solution is (15, 5).

Example problem related to general slope form:

Find the slope of the equation and then find the slope-intercept form of an Equation through the given points (0, 2) and (3, 8)?

Solution:

(x1 , y1)= (0, 2)

(x2 , y2)= (3, 8)

From the slope formula,

m= (y2-y1)/(x2-x1)

m= (8-2)/(3-0)

m=6/3

m=2

Substitute m=2 and one point (0,2)  in the below equation,

y - y1 = m(x - x1)

y - 2= 2*(x - 0)

y - 2 = 2x

y = 2x + 2

This is the general slope intercept form for the given two points.

Here, m= slope =2 and y-intercept b=2.