CBSE Class 9 Math, CBSE- Linear Equations In Two Variables

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CBSE Class 9 Math, CBSE- Linear Equations in two variables

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Class IX MathNotes for Linear Equations in Two Variables An equation of the form ax + by + c = 0 where a, b, c are real numbers, a ≠ 0, b ≠ 0 and x, y are variables is called a linear equation in two variable. Anys pair of values ofxandywhich satisfies the equation ax + by + c = 0, wherea, b, c are non-zero real numbers, is called a solution of the equation • A linear equation in two variables has infinitely many solutions. • Every point on the graph of a linear equation in two variables is a solution of the equation. Geometric representation of ax + c = 0 as an equation • in one variable is • in two variable is a.x + 0.y = –c. • If a ≠ 0, c ≠ 0 and b = 0. The equation ax + by + c �� 0 reduces to ax + c = 0 or The graph is a straight line. Parallel to y-axis and passing through the point • If b ≠ 0, c ≠ 0 and a ≠ 0. The equation ax + by + c = 0 reduces to by + c = 0 or The graph is a straight line parallel to x axis and passing through the point • If a ≠ 0, b ≠ 0, c = 0 . The equation ax + by + c = 0 reduces to ax = 0 i.e. x= 0. The graph is y-axis itself • If a = 0, b ≠ 0, c = 0. The equation ax + by + c = 0 reduces to by = 0 i.e. y= 0. The graph is x-axis itself • If c = 0 , the equation ax + by + c = 0 reduces to ax + by = 0. The graph is a line passing through origin.

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