Question

(iv)
√3x + √2y = √3
√5x + √3y = √3​

Answer 1

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!

__________