What are Linear Equations In Two Variables?
Each linear equation in two variables can be defined in a straight line. To solve a system of two linear equations in two variables, we graph both equations in the same coordinate system. The equation that can be represented in the form of px + qy + r = 0 is called a two variable linear equation. [where p, q & r are real, and p & q are not 0]. For example: 2.5p + 3q = 9, x + 8y = 9, 9u – 15v = 19, etc. Linear equations in two variables class 9 notes are provided here to help learners understand the concepts of this chapter in an easy manner.
There are infinitely many solutions possible for a linear equation in 2 variables. The graph of such equations is always a straight line. In a two variable linear equation, x = 0 denotes the equation of y-axis and y = 0 denotes the equation of the x-axis. The graph of equation x = c represents a straight line parallel to the y-axis.
Similarly, the graph of equation y = c represents a straight line parallel to the x-axis. The equation y = cx (where c = constant) represents a line passing through the centre (origin). All the points on the graph of a 2 variable linear equation is a solution of the linear equation. The graph of a linear equation represents the solution of a linear equation. The solution remains unaffected when:
- Same quantity is either subtracted or added from both the sides (LHS and RHS) of the equation.
- If both LHS and RHS of an equation are multiplied or divided by the same non-zero number.
Q.1) Write each of the following as an equation in two variables:
(i) y = 2 (ii) x = –5 (iii) 5y = 2 (iv) 2x = 3
Q.2) Find four different solutions of the equation x + 2y = 6.
Q.3) Write four solutions for each of the following equations:
(i) πx + y = 9 (ii) 2x + y = 7 (iii) x = 4y
Q.4) The bus fare in a town is as follows: For the 1st kilometre, the bus fare is Rs.8 and for the subsequent distance it is Rs.5/km. Let the distance covered be x km and total bus fare be Rs.y. Write a linear equation for the given information, and prepare a graph.
Q.5) Vaishaki and Sameera, 2 students of 9th standard, together contributed Rs.200
towards the Relief Fund to help the flood victims. Write a linear equation and draw a graph which satisfies the above data.
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|Solving Linear Equations||Linear Equations In Two Variables|
|Application Of Linear Equations In Two Variables||Graphing Of Linear Equations|