Question

Solve the following pair of linear equations by the cross-multiplication methods:

$$\begin{gathered} 8x+5y=9 \\ 3x+2y=4 \end{gathered}$$

Answer 1

On comparing the given equation

$$\begin{gathered} 8x+5y=9 \\ 3x+2y=4 \end{gathered}$$

with

$$\begin{gathered} a_{1}x+b_{1}y+c_1=0 \\ {a}_{2}x+b_{2}y+c_2=0 \end{gathered}$$

On using cross multiplication method, we have,

$\frac{x}{b_1{c}_2-b_2{c}_1}=\frac{y}{c_1{a}_2-c_2{a}_1}=\frac{1}{b_2{a}_1-b_1{a}_2}$

Therefore,

$$\begin{gathered} \frac{x}{(-20+18)}=\frac{y}{(-27+32)}=\frac{1}{16-15} \\ \Rightarrow \frac{-x}{2}=\frac{y}{5}=\frac{1}{1} \\ \text{So,}\frac{-x}{2}=1\Rightarrow x=-2and\frac{y}{5}=1\Rightarrow y=5 \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{2}$ and $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{5}$ is the solution of given equation.