Question

Solve, using cross-multiplication :
√2x - √3y = 0
√5x + √2y = 0

Answer 1

Given equation are √2x - √3y = 0 and √5x + √2y = 0
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, We have

a₁ = √2, b₁ = √3, c₁ = 0 and a₂ = √5, b₂ = √2, c₂ = 0

Now, x = `[ b_1c_2 - b_2c_1 ]/[ a_1b_2 - a_2b_1 ]  and  y = [ c_1a_2 - c_2a_1 ]/[ a_1b_2 - a_2b_1 ]` 

⇒ x = `[ (-sqrt3) xx 0 - sqrt2 xx 0 ]/[ sqrt2 xx sqrt2 - sqrt5 xx (-sqrt3) ]  and  y = [ 0 xx sqrt5 - 0 xx sqrt2 ]/[ sqrt2 xx sqrt2 - sqrt5 xx ( - sqrt3 ) ]`

⇒ x = `0/[ 2 + sqrt15 ] and y = 0/[ 2 + sqrt15 ]`

⇒ x = 0 and y = 0.