NCERT Class 10 Mathematics

56 MATHEMATICS Step 2 : Subtracting Equation (4) from Equation (3), (4x – 4x) + (6y – 6y) = 16 – 7 i.e., 0 = 9, which is a false ...

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 57 Form the pair of linear equations in the following problems, and find their soluti ...

58 MATHEMATICS Therefore, x = – (4)(–35) (3)( 28)✁ (5)(4) (3)(2) ✂ ✂ ✂ i.e., x = (3) (– 28) (4) ( 35) (5)(4) (2)(3) ✄ ✄ ✄ (5) If ...

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 59 i.e., (b 2 a 1 – b 1 a 2 ) x =b 1 c 2 – b 2 c 1 So, x =^1221 12 21 bc b c ab a b ...

60 MATHEMATICS 3 – 46^23 (^5) – 74 35 x y 1 Note that you can write the solution given by Equations (5) and (6) in the following ...

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 61 Then (3) ( 74) (5) ( 46) x = 1 ( 46)(3) ( 74)(2) (2)(5) (3)(3) y ✁ i.e., 222 230 ...

62 MATHEMATICS So, we need 12 k = 33 k kk ✁ or, 12 k = 3 k which gives k^2 = 36, i.e., k = ± 6. Also, 3 k = k 3 k ✂ gives 3k = ...

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 63 (i) A part of monthly hostel charges is fixed and the remaining depends on the numb ...

64 MATHEMATICS These equations are not in the form ax + by + c = 0. However, if we substitute (^11) pand q xy in Equations (1) ...

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 65 Equations (3) and (4) form a pair of linear equations in the general form. Now, you ...

66 MATHEMATICS Let t 2 be the time, in hours, taken by the boat to go 44 km downstream. Then 2 t^44. x y ✁ The total time taken ...

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 67 Hence, the speed of the boat in still water is 8 km/h and the speed of the stream i ...

68 MATHEMATICS EXERCISE 3.7 (Optional)* The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as ...

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 69 3.6 Summary In this chapter, you have studied the following points: 1. Two linear e ...

4 4.1 Introduction In Chapter 2, you have studied different types of polynomials. One type was the quadratic polynomial of the f ...

QUADRATIC EQUATIONS 71 Sridharacharya (A.D. 1025) derived a formula, now known as the quadratic formula, (as quoted by Bhaskara ...

72 MATHEMATICS Therefore, their product = (x – 5) (40 – x) =40x – x^2 – 200 + 5x =– x^2 + 45x – 200 So, – x^2 + 45x – 200 = 124 ...

QUADRATIC EQUATIONS 73 (ii) Since x(x + 1) + 8 = x^2 + x + 8 and (x + 2)(x – 2) = x^2 – 4 Therefore, x^2 + x + 8 =x^2 – 4 i.e., ...

74 MATHEMATICS (ii) The product of two consecutive positive integers is 306. We need to find the integers. (iii) Rohan’s mother ...

QUADRATIC EQUATIONS 75 Note that we have found the roots of 2 x^2 – 5x + 3 = 0 by factorising 2 x^2 – 5x + 3 into two linear fac ...