Question

Solve, using cross-multiplication :
4x + 6y = 15
3x - 4y = 7

Answer 1

Given equation are 4x + 6y = 15 and 3x - 4y = 7
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, We have

a₁ = 4, b₁ = 6, c₁ = -15 and a₂ = 3, b₂ = - 4, 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 = `[ 6 xx (-7) - ( - 4 ) xx ( - 15 )]/[ 4 xx (-4) - 3 xx 6 ]  and  y = [ - 15 xx 3 - ( - 7 ) xx 4 ]/[ 4 xx ( - 4 ) - 3 xx 6 ]`

⇒ x = `[ - 42 - 60 ]/[ -16 - 18]  and y = [ - 45 + 28 ]/[ - 16 - 18 ]`

⇒ x `(-102)/-34  and y = (-17)/(-34)`

⇒ x = 3 and y = `1/2`