Class 10 Mind Map Maths Pair of Linear Equations in Two Variables

CHAPTER Pair of Linear Equations 3 in Two Variables KEY POINTS Linear equation in two variables a1x + b1y + c1 = 0 … (1) a2x + b2y + c2 = 0 … (2) Equation reducible Equation of a to a pair of linear straight line equation Method to solve ax + by + c = 0 2 3 5 4 Solution (x, y)  Points x + y = 13, x + y =2 lying on straight line, Algebraic Graphical 1 1 method method Put x = 0, y = b y 0 2a + 3b = 13, 5a + 4b = 2 c= + by a1 b1 Intersecting lines a + b + ax x' x 2 2 0 (intersect at 1 point) one solution a b c Coincident a = b = c 1 1 1 y' Elimination Method 2 2 2 a1x + b1y = c1 …(1) Coincide Infinite solution Cross multiplication a b c a2x + b2y = c2 …(2) method Parallel lines a = b = c 1 1 1 Substitution Method Multiplying eq. (1) by a2 2 2 2 a1x + b1y + c1 = 0 …(1) b1 x c1 y a1 1 b1 (Not Non Intersecting) No solution and eq. (2) by a1 making a2x + b2y + c2 = 0 …(2) coefficient of x same and b2 c2 a b2 x y 2 Substituting the value of hence eliminating x and b1c2 – b2c1 = c a – a c = a 1b – b a x from eq. (1) in eq. (2) finding y. 1 2 1 2 1 2 1 2 and finding y and b1c2 – b2c1 x = ab –b a vice versa. 1 2 1 2 c1a2 – a1c2 y = ab –b a 1 2 1 2 VERY SHORT ANSWER TYPE QUESTIONS 1. If the lines given by 3x + 2ky = 2 and 2x + 5y = 1 are parallel, then the value of k is _______ . 2. If x = a and y = b is the solution of the equation x – y = 2 and x + y = 4, then the values of a and b are respectively _______ . Mathematics-X 27