Question

Solve, using cross-multiplication :
8x + 5y = 9
3x + 2y = 4

Answer 1

Given equation are 8x + 5y = 9 and 3x + 2y = 4
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, We have

a₁ = 8, b₁ = 5, c₁ = -9 and a₂ = 3, b₂ = 2, c₂ = - 4

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 = `[ 5 xx ( - 4 ) - 2 xx ( - 9 )]/[ 8 xx 2 - 3 xx 5 ]  and  y = [ - 9 xx 3 - ( - 4 ) xx 8 ]/[ 8 xx 2 - 3 xx 5 ]`

⇒ x = `[ - 20 + 18 ]/[ 16 - 15 ] and y = [ - 27 + 32 ]/[ 16 - 15 ]`

⇒ x = `-2/1 and y = 5/1`
⇒ x = - 2 and y = 5.