Question

x+y=5
2x-3y=4
solve by cross multiplication method​

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of equations are

• x + y = 5

• 2x - 3y = 4

By using Cross Multiplication method,

$\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf 2 & \bf 3 & \bf 1& \bf 2\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf 1 & \sf 5& \sf 1 & \sf 1\\ \\ \sf - 3 & \sf 4 & \sf 2 & \sf - 3\\ \end{array}} \\ \end{gathered}$

Now,

$\rm :\longmapsto\:\dfrac{x}{4 - ( - 15)} = \dfrac{y}{10 - 4} = \dfrac{ - 1}{ - 3 - 2}$

$\rm :\longmapsto\:\dfrac{x}{4 + 15} = \dfrac{y}{6} = \dfrac{ - 1}{ - 5}$

$\rm :\longmapsto\:\dfrac{x}{19} = \dfrac{y}{6} = \dfrac{ 1}{ 5}$

On taking second and third member, we get

$\rm :\longmapsto\: \dfrac{y}{6} = \dfrac{ 1}{ 5}$

$\bf\implies \:y = \dfrac{6}{5}$

On taking first and third member, we get

$\rm :\longmapsto\:\dfrac{x}{19} = \dfrac{1}{5}$

$\bf\implies \:x = \dfrac{19}{5}$

$\begin{gathered}\begin{gathered}\bf\: \bf :\longmapsto\:Hence-\begin{cases} &\sf{x = \dfrac{19}{5} } \\ \\ &\sf{y = \dfrac{6}{5} } \end{cases}\end{gathered}\end{gathered}$