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Example 17 - Solve: 2/x + 3/y = 13, 5/x - 4/y = -2 - Examples

Example 17 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Example 17 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3 Example 17 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4

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Example 17 Solve the pair of equations: 2/𝑥+ 3/𝑦=13 5/𝑥−4/𝑦=−2 2/𝑥+ 3/𝑦=13 5/𝑥−4/𝑦=−2 So, our equations become 2u + 3v = 13 5u – 4v = –2 Hence, our equations are 2u + 3v = 13 …(3) 5u – 4v = – 2 …(4) From (3) 2u + 3v = 13 2u = 13 – 3V u = (13 − 3𝑣)/2 Putting value of u (4) 5u – 4v = - 2 5((13 − 3𝑣)/2)−4𝑣=−2 Multiplying 2 both sides 2 × 5((13 − 3𝑣)/2)−"2 ×" 4𝑣="2 ×"−2 5(13 – 3v) – 8v = –4 65 – 15v – 8v = –4 – 15v – 8v = – 4 – 65 – 23v = – 69 v = (−69)/(−23) v = 3 Putting v = 3 in (3) 2u + 3v = 13 2u + 3(3) = 13 2u + 9 = 13 2u = 13 – 9 2u = 4 u = 4/2 u = 2 Hence, u = 2, v = 3 is the solution But we have to find x & y u = 𝟏/𝒙 2 = 1/𝑥 x = 𝟏/𝟐 v = 𝟏/𝒚 3 = 1/𝑦 y = 𝟏/𝟑 Hence, x = 1/2 , y = 1/3 is the solution of the given equation

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.