Question

Solve, using cross-multiplication :
6x + 7y - 11 = 0
5x + 2y = 13

Answer 1

Given equation are 6x + 7y - 11 = 0 and 5x + 2y = 13
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, We have

a₁ = 6, b₁ = 7, c₁ = -11 and a₂ = 5, b₂ = 2, c₂ = -13

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 = `[ 7 xx ( - 13) - 2 xx ( - 11 )]/[ 6 xx 2 - 5 xx 7 ]  and  y = [ - 11 xx 5 - ( - 13 ) xx 6 ]/[ 6 xx 2 - 5 xx 7 ]`

⇒ x = `[ - 91 + 22 ]/[ 12 - 35 ]  and y = [ - 55 + 78 ]/[ 12 - 35 ]`

⇒ x = `[ - 69 ]/[ -23 ]  and y = [ 23 ]/[ -23 ]`
⇒ x = 3 and y = -1