Question

Solve, using cross-multiplication :
4x - y = 5
5y - 4x = 7

Answer 1

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

a₁ = 41, b₁ = - 1, c₁ = - 5 and a₂ = - 4, b₂ = 5, c₂ = - 7

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 = `[ -1 xx ( - 7 ) - 5 xx ( - 5 ) ]/[ 4 xx 5 - ( - 4 ) xx (-1) ]  and  y = [ (-5) xx (-4) - ( -7 ) xx 4 ]/[ 4 xx 5 - ( - 4) xx (-1) ]`

⇒ `x = [ 7 + 25 ]/[ 20 - 4 ]  and y = [ 20 + 28 ]/[ 20 - 4  ]`

⇒ x = `32/16  and y = 48/16`

⇒ x = 2 and y = 3