Question

Cross multiplication 3x+4y=10 & x-y=1

Answer 1

Solution

Cross Multiplication Method

$a_1x\:+\:b_1y\: +\:c_1\: =\: 0$

$a_2x\:+\:b_2y\: +\:c_2\: =\: 0$

$\dfrac{x}{b_1c_2\:-\: b_2c_1}\: =\:\dfrac{y}{c_1a_2\:-\: c_2a_1}\:=\:\dfrac{1}{a_1b_2\:-\: a_2b_1}$

Now,

1st Equation

$a_1$ = 3

$b_1$ = 4

$c_1$ = - 10

2nd Equation

$a_2$ = 1

$b_2$ = - 1

$c_2$ = - 1

Now Put the value in Equation,

$\dfrac{x}{4.(-1)\:-\: (-1)(-10)}\: =\:\dfrac{y}{(-10).(1)\:-\: (-1).(3)}\:=\:\dfrac{1}{(3).(-1)\:-\: (1).(4)}$

$\dfrac{x}{-4\:-\:10}\: =\:\dfrac{y}{(-10)\:+\:3}\:=\:\dfrac{1}{-3\:-\: 4}$

$\dfrac{x}{-14}\: =\:\dfrac{y}{-7}\:=\:\dfrac{1}{-7}$

First solution :

$\dfrac{x}{-14}\:=\:\dfrac{1}{-7}$

$x\:=\:\dfrac{-14}{-7}$

$x\:=\:2$

Second Solution :

$\dfrac{y}{-7}\:=\:\dfrac{1}{-7}$

$y\:=\:\dfrac{-7}{-7}$

$y\:=\:1$

ANSWER

$\boxed{x\:=\:2}$

$\boxed{y\:=\:1}$