Question

3x-5y=6, 2x+3y=61 find the value of x and y by cross multiplication method

Answer 1

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

Given pair of linear equations are

$\rm :\longmapsto\:3x - 5y = 6 - - (1)$

and

$\rm :\longmapsto\:2x + 3y = 61 - - (2)$

Using Cross Multiplication method

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered} \begin{array}{|c|c|c|c|} \bf{2} & \bf{3}& \bf{1}& \bf{2} \\ \\ -5&6&3& -5\\ \\3&61&2&3\end{array}\end{gathered}$

$\rm :\longmapsto\:\dfrac{x}{ - 305 - 18} = \dfrac{y}{12 - 183} = \dfrac{ - 1}{9 + 10}$

$\rm :\longmapsto\:\dfrac{x}{ - 323} = \dfrac{y}{ - 171} = \dfrac{ - 1}{19}$

$\rm :\longmapsto\:\dfrac{x}{ - 323} = \dfrac{y}{ - 171} = \dfrac{1}{ - 19}$

On multiply each term by - 19, we get

$\rm :\longmapsto\:\dfrac{x}{17} = \dfrac{y}{9} = \dfrac{1}{1}$

$\bf\implies \:x = 17 \: \: \: \: and \: \: \: \: y = 9$

Additional Information :-

There are 4 methods to solve this type of pair of linear equations.

• 1. Method of Substitution

• 2. Method of Eliminations

• 3. Method of Cross Multiplication

• 4. Graphical Method