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Example 9 - Let us consider Example 2 in Section 3.3 - Substitution

  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
  2. Serial order wise
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Example 9 Let us consider Example 2 in Section 3.3, i.e., the cost of 2 pencils and 3 erasers is Rs 9 and the cost of 4 pencils and 6 erasers is Rs 18. Find the cost of each pencil and each eraser. Let the cost of pencil be x. & Let the cost of eraser be y. Romila purchased 2 pencils & 3 erasers for Rs 9 i.e. 2 × (Cost of pencil) + 3 × (Cost of eraser) = 9 2x + 3y = 9 Also, Sonali purchased 4 pencils and 6 erasers for Rs 18 i.e. 4 × (Cost of pencil) + 6 × (Cost of eraser) = 18 4x + 6y = 18 So our two equations are 2x + 3y = 9 ...(1) 4x + 6y = 18 …(2) From (1) 2x + 3y = 9 2x = 9 – 3y x = ((9 − 3𝑦)/2) Putting value of x in (2) 4x + 6y = 18 4((9 − 3𝑦)/2)+6𝑦=18 2 (9 – 3y) + 6y = 18 18 – 6y + 6y = 18 18 = 18 It is true for all values of x & y. Note : We can not obtain the specific value of x & y, because both the equation given are same. Reason :- The 2 equations given in question are 2x + 3y = 9 …(1) 4x + 6y = 18 …(2) From (2), 4x + 6y = 18 Diving both sides by 2 4𝑥/2 + 6𝑦/2 = 18/2 2x + 3y = 9 Which is equation same as equation (1) Hence both equation actually same So there can be infinite values of x and y So there can be infinite values of x and y For e.g. If y = 1, 2x + 3(1) = 9 2x + 3 = 9 2x = 9 – 3 2x = 6 x = 6/2 x = 3 And so on .

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