(a) Definition (b) Methods of solution (c) cbse maths X sample guess papers
Definition
An equation of the form ax + by + c = 0, where a, b, c are real numbers and a, b not equal to 0 is called linear equation in two variables x and y.
Examples 3x + 4y = 0, 9x - 2y + 4 = 0, 0.5x - 0.4y + 0.9 = 0
What are simultaneous linear equations in two variables?
Two linear equations in two variables x and y are said to form a system of simultaneous linear equations if each is satisfied by the same pairs of values of the variables x and y.
Solution
A pair of values of x and y satisfying each of the equations in a given system of simultaneous linear equations in x and y is called a solution.
Consistent and inconsistent
System of two linear equations in two variables is said to be consistent if it has at least one solution.
System of two linear equations in two variables is said to be inconsistent if it has no solution.
1. Graphical Method
2. Substitution Method
3. Elimination by equating the coefficients
4. Cross Multiplication
5. Method of comparision
1. graphical Method In this method two tables with points corresponding to the two equations are drawn.The points of the table are plotted on the same graph.The points of the two tables are joined together separately to get the required lines.
We can get three types of possibilities for the two lines on the graph.
(a) Two lines intersect at a point.
(b) Two lines may coincide (overlap)
(c) Two lines may be parallel.
2. Substitution Method In this method we find value of one variable from one equation and substitute in the second equation.
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