Solve: 2 x + 3 y = 13 and 5 x - 4 y = - 2

Given, 2 x + 3 y = 13 ⇒ 2 y + 3 x x y = 13 ⇒ 2 y + 3 x = 13 x y . . . . 1 5 x - 4 y = - 2 ⇒ 5 y - 4 x x y = - 2 ⇒ 5 y - 4 x = - 2 x y . . . . 2 Multiply equation ( 1 ) with 4 , ⇒ 8 y + 12 x = 52 x y . . . . 3 Multiply equation 2 with 3 , ⇒ 15 y - 12 x = - 6 x y . . . . 4 Adding equation ( 3 ) and ( 4 ) , ⇒ 8 y + 12 x + 15 y - 12 x = 52 x y - 6 x y ⇒ 23 y = 46 x y ⇒ 1 = 2 x ⇒ x = 1 2 Putting this in equation ( 1 ) , ⇒ 2 y + 3 1 2 = 13 1 2 y ⇒ 2 y + 3 2 = 13 2 y ⇒ 13 2 y - 2 y = 3 2 ⇒ 9 y 2 = 3 2 ⇒ y = 3 9 = 1 3 Hence, x = 1 2 and y = 1 3

Solve, 1 2 x + 1 3 y = 2 1 3 x + 1 2 y = 13 6

Given 1 2 x + 1 3 y = 2 1 3 x + 1 2 y = 13 6 Let, 1 x = p and 1 y = q p 2 + q 3 = 2 3 p + 2 q = 12 . . . . . 1 Similarly, p 3 + q 2 = 13 6 2 p + 3 q 6 = 13 6 2 p + 3 q = 13 . . . . . 2 Multiplying 1 by 2 and 2 by 3 ,we get 6 p + 4 q = 24 . . . . 3 6 p + 9 q = 39 . . . . 4 By subtracting 3 by 4 6 p + 4 q - 6 p - 9 q = 24 - 39 - 5 q = - 15 q = 3 By putting value q = 3 in 1 ,we get 3 p + 2 × 3 = 12 3 p = 6 p = 2 Hence, x = 1 2 and y = 1 3

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The equation $y = 3 x + 5$ has

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Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

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Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

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Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

The point of the intersection of the graph of the equations

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Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

Solve,

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Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

Find the number of solutions of a pair of linear equation

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Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

Which of the following equations has the solution of

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Mathematics>Algebra>Linear Equations in Two Variables>Solution of a Linear Equation

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A zoo has few number of penguins and polar bears. The total number of heads of both of them is

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Important Questions on Linear Equations in Two Variables

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