Mathematics
Find the equation of the straight line passing through the origin and through the point of intersection of the lines 5x + 7y = 3 and 2x - 3y = 7.
Straight Line Eq
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Answer
5x + 7y = 3 ….(i)
2x - 3y = 7 ….(ii)
Multiply (i) by 3 and (ii) by 7,
15x + 21y = 9 ….(iii)
14x - 21y = 49 ….(iv)
Adding (iii) and (iv) we get,
⇒ 29x = 58
⇒ x = 2.
Substituting x = 2 in (i), we get
⇒ 5(2) + 7y = 3
⇒ 10 + 7y = 3
⇒ 7y = 3 - 10
⇒ 7y = -7
⇒ y = -1.
Hence, the point of intersection of lines is (2, -1).
The equation of the line joining (2, -1) and (0, 0) will be given by two-point form i.e.,
Putting values in above equation we get,
Hence, the equation of the line is x + 2y = 0.
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