Question

Solve, using cross-multiplication :
3x + 4y = 11
2x + 3y = 8

Answer 1

Given equations are 3x + 4y = 11 and 2x + 3y = 8
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, we have
a₁ = 3, b₁ = 4, c₁ = -11 and a₂ = 2, b₂ = 3, c₂ = - 8

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 = `[ 4 xx (- 8 ) - 3 xx ( - 11 )]/[ 3 xx 3 - 2 xx 4 ]  and  y = [ - 11 xx 2 - ( - 8 ) xx 3 ]/[ 3 xx 3 - 2 xx 4 ]`

⇒ `x = [ - 32 + 33 ]/[ 9 - 8 ] and y = [ - 22 + 24 ]/[ 9 - 8 ]`

⇒ x = 1 and y = 2