Class 10th mathematics(linear equations in two variables)

-
Basic Concepts with Examples
•    Linear Equation in Two Variables
An equation which can be put in the form
            ax + by + c = 0
where a, b and c are real numbers {a, b ≠ 0) is called a linear equation in two variables ‘x’ and ‘y’
•    General Form of a Pair of Linear Equations in Two Variables
General form of a linear pair of equations in two variables is:
            a1x + b1y + cx - 0 and
            a2x + b2y + c2 = 0
where a1 b1, c1, a2, b2, c2 are real numbers such that
            a12 + b12 0 and a22 + b22 0
•    Solution of a Pair of Linear Equations in Two Variables
The solution of a linear equation in two variables ‘x’ and ‘y’ is a pair of values (one for ‘x’ and other for ‘y’)
which makes the two sides of the equation equal.
There are two methods to solve a pair of linear equations:
            (i) algebraic method
            (ii) graphical method.
•    Algebraic Method
We have already studied (i) Substitution method and (ii) Elimination method. Here, we will study cross-multiplication method also.
            If a1 x + b1 y + c1 = 0
                  a2 x + b2 y + c2 = 0
form a pair of linear equations, then the following three situations can arise:
       (i) If  then the system is consistent.
       (ii) If  then the system is inconsistent.
       (ii) If  then the system is dependent and consistent.
•    Graphical Method of Solution of a Pair of Linear Equations
       (i) If the graphs of two equations of a system intersect at a point, the system is said to have a unique solution, i.e., the system is consistent.
       (ii) If the graphs of two equations of a system are two parallel lines, the system is said to have no solution, i.e., the system is inconsistent.
       (iii) When the graphs of two equations of a system are two coincident lines, the system is said to have infinitely many solutions, i.e., the system is consistent and dependent.

Comments

Post a Comment

Popular posts from this blog

Class 11th science chemistry (thermodynamics)

-
Image
Thermodynamics deals with the change of energy in physical and chemical processes. It allows us to study these changes quantitatively as well as to make effective predictions. Therefore, we divide the universe as surrounding and system. Physical or chemical processes lead to progression or immersion of heat part of it may be converted to work. According to the first law of thermodynamics , these quantities are related as ∆U = q + w where q is heat and w is work. Change in internal energy is a state function and depends on only the initial and final states. On the other hand, w and q are not state functions. The change in temperature due to the transfer of heat one system to another system can be measured. Heat evolved or absorbed is expressed as q = C∆T. In case of expansion of gas, work is measured as w = –p ex ∆V Enthalpy Change Enthalpy change is defined as the change in energy of a system at constant pressure. It is denoted as ΔH. Enthalpy is a state function. Enthalpy ch...
Read more

Class 11th science chemistry (Redox reaction)

-
Image
Redox reaction is the combination of both oxidation and reduction reactions. When redox reaction takes place, both oxidation and reduction reactions also occur simultaneously. What is a Redox Reaction? Redox is a term used for the oxidation-reduction reaction. Redox reaction is a chemical reaction where a change in the oxidation state of atoms occurs. It involves electron transfer i.e if one chemical species gains electrons, then another chemical species gives or loses electrons. The species from which the electron is lost is said to be oxidized whereas the species to which the electron is added is said to be reduced. Example zinc displaces copper in an aqueous solution called copper sulfate. Redox reactions can be classified into four different categories: Combination reaction Decomposition reaction Displacement reaction Disproportionation reaction Oxidizing And Reducing Agents The role of an oxidizing agent (Oxidant) in a chemical reaction is to gain electrons. ...
Read more