Question

Solve, using cross-multiplication :
4x - 3y = 0
2x + 3y = 18

Answer 1

Given equation are 4x - 3y = 0 and 2x + 3y = 18
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, We have

a₁ = 4, b₁ = - 3, c₁ = 0 and a₂ = 2, b₂ = 3, c₂ = -18

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 ( - 18 ) - 3 xx 0 ]/[ 4 xx 3 - 2 xx ( - 3) ]  and  y = [ 0 xx 2 - ( - 18 ) xx 4 ]/[ 4 xx 3 - 2 xx ( - 3) ]`

⇒ `x = [ 54 - 0 ]/[ 12 + 6 ]  and y = [ 0 + 72 ]/[ 12 + 6 ]`

⇒ x = `54/18 and y = 72/18`

⇒ x = 3 and y = 4.