Question

solve the following pair of linear equation by cross multiplication method:- X + 2 Y = 2 and X - 3y = 7

Answer 1

Therefore the solution of the given two equations is x=4  and y= - 1.

Step-by-step explanation:

The cross multiplication method:

$a_1x+b_1y+c_1=0$

$a_2x+b_2y+c_2=0$

The solution of the above two equation is

$\frac{x}{b_1c_2-b_2c_1}=\frac{y}{a_2c_1-a_1c_2}=\frac{1}{a_1b_2-a_2b_1}$

$\therefore x=\frac{b_1c_2-b_2c_1}{a_1b_2-a_2b_1}$    and    $y=\frac{a_2c_1-a_1c_2}{a_1b_2-a_2b_1}$

Given equation are

$x+2y=2$          $\Rightarrow x+2y-2=0$.......(1)

$x-3y=7$          $\Rightarrow x-3y-7=0$ .......(2)

Here $a_1=1$, $b_1=2$,$c_1=-2$, $a_2=1$, $b_2=-3$, $c_2=-7$

$\frac{x}{2.(-7)-(-3).(-2)}=\frac{y}{1.(-2)-1.(-7)}=\frac{1}{1.(-3)-1.2}$

$\frac{x}{-20}=\frac{y}{5}=\frac{1}{-5}$

$\therefore x= \frac{-20}{-5}=4$

$y=\frac{5}{-5}=-1$

Therefore the solution of the given two equations is x=4  and y= - 1.