Solving $2x+3y-11=0$ and $3x+2y-9=0$ by the cross-multiplication method gives:

With a₁ = 2, b₁ = 3, c₁ = −11 and a₂ = 3, b₂ = 2, c₂ = −9, the rule $x$/(b₁c₂ − b₂c₁) = $y$/(c₁a₂ − c₂a₁) = 1/(a₁b₂ − a₂b₁) gives $x/(-27+22)=y/(-33+18)=1/(4-9)$, i.e. $x/(-5)=y/(-15)=1/(-5)$. So $x=1$ and $y=3$. Check: 2 + 9 = 11 and 3 + 6 = 9.