Question

Solve, using cross-multiplication :
x - y + 2 = 0
7x + 9y = 130

Answer 1

Given equation are x - y + 2 = 0 and 7x + 9y = 130
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, We have

a₁ = 1, b₁ = -1, c₁ = 2 and a₂ = 7, b₂ = 9, c₂ = -130

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 (- 130) - 9 xx 2 ]/[ 1 xx 9 - 7 xx ( - 1 ) ]  and  y = [ 2 xx 7 - ( - 130 ) xx 1 ]/[ 1 xx 9 - 7 xx ( - 1) ]`

⇒ x = `[ 130 - 18 ]/[ 9 + 7 ]   and  y = [ 14 + 130 ]/[ 9 + 7 ]`

⇒ x = `[ 112 ]/[ 16 ]   and y = [ 144 ]/[ 16 ]`

⇒ x = 7 and y = 9.