# Archive for October, 2011

## Solving Problems of Linear Equations

In mathematics every problem is represented in the form of an equation of variables, integer coefficients and operators, and all of these equations are categorized as linear or non- linear equations. For solving non- **linear equations** they are somehow converted into a linear form.

Friends today we are going to discuss about **linear equations** and **linear equations** graph. Every linear equation represents a straight line with several parallel conditions on a 2D plane. As we know **linear equations** consist of no. of derivatives which are formed by variables with or without integer coefficient but there is one necessary condition of forming **linear equations** is that all of its derivatives must be in same order of degree. The standard form of any linear equation is as:

Ax + By = C

Here ‘A’, ‘B’ and ‘c’ are integer constants and ‘x’, ‘y’ are two unknown variables of same order.

For graphing of any linear equation following conditions must be satisfied:

1) The equation should be of standard form

2) Linear equation must consist of two unknown variables which represents x and y axis coordinated which are required to graph any linear equation on a 2D plane.

Let us take an example for **linear equation graph** representation:

Given equation is ——> x^{2} + 9 = y^{2}

First convert it into standard form as:

x^{2} + y^{2} = 9

Now for finding x= axis co-ordinates, put y =0 in the equation

So, x^{2} = 9

x = +3 or – 3

Now for y co-ordinates, put x= 0 in equation

y^{2} = 9

y = +3 or -3

At last we have coordinated of (x, y) as (+3. +3) and (-3, -3), from which we can draw **linear equation graph**.

For more problems on **linear equations**, students can take lessons which cover **linear equations **topics of TutorVista, an online math tutoring websites .TutorVista provides **online help** to students across the globe for solving their math related queries in a quick time and explained manner.

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## Solving and graphing linear equations

Mathematics is a subject in which problems are represented in the form of equations. An equation is a combination of variables with constant coefficient or without it and constants which are related by arithmetic operators. Friends, today we are going to cover the **linear equations** topics of TutorVista. Linear equations are form of algebraic equation in which all the derivatives are of same order. Let us take an example of** linear equations in two variables**:

2x^{2}+ 3y^{2}= 2

Here 'x' and 'y' are two variables and both are of 2nd order.

Every linear equation represents a straight line but with several conditions and according to these conditions **linear equations** have some basic forms as standard form, slope intercept form, parametric form and polar form. Let us see standard form of** linear equations** of two variables

y = mx + c

here 'x' and 'y' are variables and 'm' is a constant representing slope of the line with constant 'c'.

For **graphing linear equations** both 'x' and 'y' intercept are required of the straight line forming by that linear equation and for finding these co-ordinates a simple principle is followed which states all the y points of equation are 0 on the x- axis and similarly all the x points of equations are 0 on y – axis.

Lets take an example and see how to implement this principle to find x and y co- ordinates of the** linear equations**:

x^{2}+ 2y^{2} = 4

so at x- axis , y= 0 than

x^{2}= 4

x = +2 or -2

now on y- axis , x = 0 than

2y^{2}= 4

y^{2}= 2

y = +(2)1/2or – (2)1/2

So the co-ordinates are ( 2, (2)1/2)and (-2,( -2)1/2) and from this you can graph** linear equations**.

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## TutorVista help in Linear Equations

Friends! Today we all are going to learn about ** Linear equations** in mathematics. Now the first question comes in our mind is, What is an Equation ? An equation is basically a condition on the variable. In simple mathematical manner we can say that any equation that when graphed produces a straight line, then the equation is called as

**Linear equation**.

The common form of a **Linear equation** in the two variables like x and y is…..

y = mx + b where x and y are two variables and m and b are two constants.

The constant m determine s the slope or gradient of that line and the constant b shows the point at which line crosses the Y-axis. Constant b also known as Y-Intercept. Now we are going to discuss about **Linear Inequality**.In graphical manner, we can say that a **linear inequality** describes an area of the coordinate plane that has a boundary line. In simple way, in **Linear Inequalities** everything on one side of a line on a graph. In mathematics, a **linear inequality** is an inequality which involves a linear function. For solving inequalities we need to learn the symbols of inequalities like the symbol < means less than and the symbol > means greater than and the symbol Ã¢ÂÂ¦ or ≤ less than or equal to etc. Let’s see about some examples of **Linear problem**s : -6 < x – 4 < 12

-6 < x – 4 < 12

add 4 to all 3 parts

-2 < x <16

divide 2 from all 3 parts

-2 < x < 16

To graph the following equation, you put an open circle or we can say mark it by a dot on the point (2,0) and then you put an open circle on the point (16,0).Then draw a line between the two.

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## Equation solver removes maths Obstacles

Friends! all of us want to secure maximum marks in his/her exams but some of the students are scared of mathematics. Most of the higher grade students are afraid of math topics like **linear inequalities** and system of linear equations, so online math solvers are available for solving your problems. This article is about the different types of equations and how to solve the equation in a better, easier and in faster manner.

Now we are going to discuss about linear equations. In simple mathematical manner, we can say that any equation that when graphed produces a straight line, then the equation is called as Linear Equation. The common form of a linear equation in the two variables like x and y is

y = mx + b

where x and y are two variables and m and b are two constants. The constant m determines the slope or gradient of that line and the constant b shows the point at which line crosses the Y-axis. Constant b also known as Y-Intercept.

**Linear equations** with inequality signs are called as linear inequalities. An inequality tells that two values are not equal. For example a ≠ b shows that a is not equal to b. A linear inequality describes an area of the coordinate plane that has a boundary line. In simple way in linear inequalities everything is on one side of a line on a graph. In mathematics, a linear inequality involves a linear function. For solving inequalities, we need to learn the symbols of inequalities like the symbol < means less than and the symbol > means greater than and the symbol Ã¢ÂÂ¦ or ≤ less than or equal to etc.

A system of equations come with the relationship between two or more functions, which can be used to form a number of real-world situations. It is basically a collection of two or more equations with a same set of unknowns. **Systems of Equations Solvers** are available online which generates answer on one click by user on solve option and also shows the student how to arrive at the answer.

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## Covers Linear Equations topics of TutorVista

Tutorvista is a website designed specially for the kids who face problem while doing math sums and solving mathematical questions. Tutorvista covers many key definitions and phrases which help you in solving math problems. Algebra is the base of mathematics and one need to be strong in algebra if he/she wants to get mastery in mathematics. Lets have a look on what is algebra, expressions and linear equations. Algebra is a imperative branch of mathematics that substitutes letters for numbers.

In this, symbols usually letters of alphabets represents numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all the members of the set. Algebra includes real numbers, complex numbers. matrices, vectors, and many more topics.

Now, lets talk about algebraic expression, it is a number or variable, or combination of the two connected by some mathematical operators like addition, subtraction, multiplication, division, exponents roots and so on. An **algebraic expression** includes variables, constants and operating symbols. Algebraic expressions is a phrase, not a mathematical sentence, so it does not contain an equal to symbol.

For example:- 2y^{2}+ 2x + 4xy + 5

Here, terms are the elements separated by the plus or minus symbol. In this example, we have four terms,2y^{2}, 2x, 4xy and 5. Terms may include constants, variables or coefficients. And when we solve the algebraic expressions, we replace the variables with the given numbers and performs the indicated operations.

Large number of equations are embedded in algebra. Equation is a mathematical statement and it contains a equal (=) symbol. Linear equations are the simplest type of algebraic equations and **differential equations** are the toughest one.** Linear equations** are the equations that involves one or more variables and its graph is always a straight line. In linear equation each term is either a constant or the product of constant and the power of the single variable. While a differential equation is an equation that expresses a relationship between functions and their derivatives. You can easily learn all the above topics, using tutorvista’s math help and can become master of the subject.

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