One of the most important and conceptual question from linear equations in two variables in which we have to find the value of variables x and y from the equations 5/x+6y=13, 3/x+4y=7
RS Aggarwal, Class 10, chapter 3B, question no 18
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The given equations are:
5/x + 6y = 13 ……..(i)
3/x + 4y = 7 ……..(ii)
Putting 1/x = u, we get:
5u + 6y = 13 …….(iii)
3u + 4y = 7 ……(iv)
On multiplying (iii) by 4 and (iv) by 6, we get:
20u + 24y = 52 ……..(v)
18u + 24y = 42 ……..(vi)
On subtracting (vi) from (v), we get: 2u = 10
⇒ u = 5
⇒ 1/x = 5
⇒ x = 1/5
On substituting x = 1/5 in (i), we get:
5/ 1/3 ⁄ + 6y = 13
25 + 6y = 13
6y = (13 – 25) = -12
y = -2
Hence, the required solution is
x = 1/5 and y = -2