Linear Equations in XI Grade

After giving you the whole introduction of grade XI syllabus, its time to start the real demonstration of each topic. Today we are starting with first topic that puts variety of problems in front of students like you and that is Linear equations and linear inequalities. Also improve your skills with graphing linear equations. When students are promoted into XI th standard that time the only thing strikes in their mind is the increased level of math queries. Although they have study most of the topics in their earlier classes but still nothing gonna be easy for them and the scenario starts with Linear equations. Before grade XI math, students are used to with simplification of linear equations but here they have to represent it with graphs and most importantly first they have to convert into linear form from corresponding non-linear form.

Let us discuss “ why linear equations are always taken as the most important factor of mathematics?” Answer is that everything, which is predefined, students learn to solve various kind of queries made by performing much deep analysis on Linear form of mathematical queries thats the reason why all the standard formulas and principles are directly implacable on the linear equations. But here another question arises that “ what to do with Non-linear equations of mathematics?” As we know that the list of formulas we have, will not be useful to solve non-linear form so in this case students has to convert the non-linear query into its appropriate linear form. For more information on linear equations visit this.

We will see how this is to be done in remaining article, Another point is that mathematics is a vast subject and includes several types of equations, so it is clear that there are variety of standard forms. The basic form of any linear equation is as:

Ax + By = C

here 'A', 'B' and 'C' is integer coefficients and x and y are variables.

Let us take an equation:

2x =c

Now if the above equation is seen that it is linear form but you guys must be thinking that it is not matching with the above standard equation, but it is.

Let us see how,

Ax + By = C :: 2x =c

Here A = 2 , B = 0 ( that's why y derivative is automatically discarded from the equation)

So most of the times students fix them only because they are unable to understand the right form of the equation.

As this one is the part of Algebra so the objective of the equation solving is very much clear to students and that is to determine the numerical values of Variables of the equations. Let us take an example and see the normal evaluation process of any linear equation form:

We are going to take system of linear equation rather then a single one because this is the demand of grade XI math,

10x1 - 7x2 = 7

-3x1 + 2x2 + 6x3 = 4

5x1 - x2 + 5x3 = 6

When you have to deal with system of linear equations, that time the system evaluation is possible when the number of equations are equal to the number. of unknown variables in the system. In similar way here three equations are included in system and the 3 unknown variables are to be evaluated. Now its up to you how to solve this equations, either by normal arithmetic process or by matrix use. Today we are going to see both ways, first start with matrix way

10 -7 0 x1 7

-3 2 6 x2 4

5 1 5 x3 6

According to the algorithm, elimination of the variables is done like x1 is to be eliminated from first equation, x2 is from second and x3 from third. This is done to convert the whole system into more proper linear form. Let's see the actual execution of this:

by adding 0.3 times the first equation to the second equation and subtracting 0.5 times the first equation from the third

equation. This will covert the matrix as following:

10 -7 0 x1 7

0 -0.1 6 x2 6.1

0 2.5 5 x3 2.5

Now to eliminate x2 from second equation we are implementing two steps for executing with more ease:

10 -7 0 x1 7

0 2.5 5 x2 2.5

0 -0.1 6 x3 6.1

In the above matrix we had exchanged the last two rows because the pivot element ( -0.1) less than the next one (2.5), this process is called pivoting. Now for eliminating x2 from second equation, add 0.04 times of the second equation to the third equation and the resultant one is :

10 -7 0 x1 7

0 2.5 5 x2 2.5

0 0 6.2 x3 6.2

From the above matrix, the last equation is:

6.2 x3 =6.2

x3 = 1

Now substitute this value in the second equation, then

2.5 x2 + (5)(1) = 2.5

2.5 x2 = - 2.5

x2 = -1

The determination of x1 easily can be done by substituting the value of x2 and x3 in first equation:

10 x1 + (¡7)(¡1) = 7

x1= 0

So the solution of the system of linear equation

0

x= -1

1

This is all about linear equations. Let's move towards the additional section of this topic that is Inequalities. Presentation of linear inequalities is almost similar to the linear equations but the only replacement is the equality sign with any of inequality symbol. But this only change in equation format causes a bigger difference in the answer although the solution process is pretty similar as well. The answer of inequality equation is a range rather then a fixed value. While solving any linear inequity, students need to implement some of the predefined fundamentals that are:

1. Additional property : If p<b and c is any real number, then p + c< b + c.

  For example, -2<-1 implies -2+4<-1 + 4.

2. Multiplication property: If p<b and c is positive, then pc<bc.

For example, 1<3 implies 1(4)< 3(4).

3. If p<b and c is negative, then pc > bc.

For example, 1<9 implies 1(-2)>9(-2).

4. Transitive property :If p<b and b<c, then p< c.

For example, -1/2<3 and 3<8/3 so its imply -1/2<8/3.

Let us take an example of linear inequality:

Suppose given equation is 2 (3P + 2) -20 > 8(P - 3) 

First remove the brackets by multiplying the terms in and out of bracket,

6P + 4 -20 > 8P - 24
6P - 16 > 8P - 24 

Now add 16 to both sides

6P > 8P - 8 

Shift 8P to tight hand side or subtract 8P from both sides

-2P > -8

-P > -4

Now multiply with (–) sign, this will cause reverse if inequality symbol

P< 4

This reveals that the solution of the equation has the region from (-infinity) to less than 4.

This is how linear inequalities are being resolved. To learn more about linear equations and inequalities students can take the assistance of various online math tutors. These Online math tutoring providers are expert and proficient in mathematics and to extract the best result, number of online math tutors are categorized according to the various branches of mathematics. For example whenever you ask for help in linear equation or inequalities then an Algebra tutor will cover it. The common reason for most of the students for demanding that extra assistance, is the environment in the class room that creates lots off hesitation in students mind to ask queries. Online math service is using such tools, which exhibits friendly environment for students to ask their doubts from online tutors without hesitation. Some of these features are Online Live chat, video conference, video seminars and online math tests to check your math skills. The most suitable facility while going for online learning is there 24 x 7 hours Active functionality. Whenever you want and wherever you are the service access is always possible through remote connection and the fluent of the connection is also pretty reliable because of trusted websites platform. Students can arrange regular lesson sessions according to their preference and option of choosing tutor from the avoidable one's also an authorized option for students.

Online tutors also provides some math calculators computer-coded programs that enhances the speedy response of their service in respect of students complex queries. These calculators solves various kind of queries in a quick while and the way they prefer to solve them in short while, also gains the knowledge of students that helps them to use short tricks in simplifying queries.

So, this is all about your first step in grade XI math, where you need to handle the queries on linear equations and inequalities. You can also play linear equations worksheets online. In this article we have explored the required fundamentals to solve these queries. Now you just need to imply the whole scenarios sequentially and to help you and other students in that process, online math educational services are always present on Internet platform.

In upcoming posts we will discuss about Absolute Value in Grade XI and perpendicular lines/planes. Visit our website for information on Maharashtra board syllabus class 11