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Pair of Linear Equations in Two Variables

Short Answer Type

51. If three times the larger of two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder. Also if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the numbers.

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52. Tanvika went to a hotel in a town with her big family. They consumed 23 idlies, ISpoories, 7 dosas and 19 vadas. the bill was Rs. 108. Next day they consumed 34 idlies, 8 vadas, 22 poories and 7 dosas. The bill came to Rs. 114 if one idilie cost same as vada. What is the cost of one poori ?

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53. Solve for ‘x’ and ‘y’:

space space space space space bx plus ay equals straight a plus straight b space semicolon space space space ax open square brackets fraction numerator 1 over denominator straight a minus straight b end fraction minus fraction numerator 1 over denominator straight a plus straight b end fraction close square brackets plus by open square brackets fraction numerator 1 over denominator straight b minus straight a end fraction minus fraction numerator 1 over denominator straight b plus straight a end fraction close square brackets equals 2

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54. Solve for ‘x’ and ‘y’:

straight b left parenthesis straight a minus straight b right parenthesis straight x minus straight a left parenthesis straight b minus straight a right parenthesis straight y equals straight a squared minus straight b squared semicolon space space ax open square brackets fraction numerator 1 over denominator straight a minus straight b end fraction minus fraction numerator 1 over denominator straight a plus straight b end fraction close square brackets plus by open square brackets fraction numerator 1 over denominator straight b minus straight a end fraction minus fraction numerator 1 over denominator straight b plus straight a end fraction close square brackets equals 2

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55. Solve the equation for ‘x’ and ‘y’ :

148 over straight x plus 231 over straight y equals 257 over xy semicolon space space 231 over straight x plus 148 over straight y equals 610 over xy

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56. Solve for ‘x’ and ‘y’ ;

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where 2x + 3y ≠ 0; 3x - 2y ≠ 0.

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57. The present age of a father is equal to the sum of the ages of his 5 children. 12 years hence, the sum of the ages of his children will be twice the ages of their father. Find the present age of the father.

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58. A and B are friends and their ages differ by 2 years. A’s father D is twice as old as A and B is twice as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B.

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59. Solve for ‘x’ and ‘y’ : ax + by = 1 ; $bx space plus space ay space equals space fraction numerator left parenthesis straight a plus straight b right parenthesis squared over denominator straight a squared plus straight b squared minus 1. end fraction$

Solution not provided.
$x equals fraction numerator a over denominator a squared plus b squared end fraction comma space space y space equals space fraction numerator a over denominator a squared plus b squared end fraction$

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60.

Solve the following system of linear equations

2(ax - by) + (a + 4b) = 0; 2(bx + ay) + (b - 4a) = 0.

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