(iv)
√3x + √2y = √3
√5x + √3y = √3
Answers
Given equations:
√3x + √2y = √3
√5x + √3y = √3
Methods to solve pair of linear equations:
Elimination method
Substitution method
Cross-multiplication method
Method to be used here:
Elimination method
Solution:
√3x + √2y = √3 ..(1)
√5x + √3y = √3 ..(2)
Multiply the whole equation (1) by √5 {Since we need to have the same coefficient of x in both the equations}
=> √5(√3x + √2y) = (√3)√5
=> √15x + √10y = √15
=> √15x = √15 - √10y ..(a)
Multiply the whole equation (2) by √3 {Since we need to have the same coefficient of x in both the equations}
=> √3(√5x + √3y) = (√3)√3
=> √15x + 3y = 3
=> √15x = 3 - 3y ..(b)
(a) = (b)
=> √15 - √10y = 3 - 3y
=> 3 - √15 = 3y - √10y
=> y = (3 - √15)/(3 - √10)
√15x = 3 - 3y
=> √15x = 3 - 3(3 - √15)/(3 - √10)
=> √15x = (3(3 - √10) - 3(3 - √15))/(3 - √10)
=> x = (9 - 3√10 - 9 + 3√15)/(3 - √10)√15
=> x = (3√15 - 3√10)/(3√15 - 5√6)
Hope it helps!
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