Question

Solve, using cross-multiplication :
4x - 3y - 11 = 0
6x + 7y - 5 = 0

Answer 1

Given equation are 4x - 3y - 11 = 0 and 6x + 7y - 5 = 0
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, We have

a₁ = 4, b₁ = - 3, c₁ = -11 and a₂ = 6, b₂ = 7, c₂ = - 5

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 = `[ - 3 xx ( - 5 ) - 7 xx ( - 11 )]/[ 4 xx 7 - 6 xx ( - 3 ) ]  and  y = [ - 11 xx 6 - ( - 5 ) xx 4 ]/[ 4 xx 7 - 6 xx ( - 3) ]`

⇒ x = `[ 15 + 77 ]/[ 28 + 18 ] and y = [ - 66 + 20 ]/[ 28 + 18 ]`

⇒ x = `92/46 and y = - 46/46`

⇒ x = 2 and y = - 1