Question

solve the following by cross multiplication method .
1) 5x + 3y=35
2x + 4y =28​

Answer 1

Solution :

$\bf{\small{\red{\underline{\bf{Given\::}}}}}$

$\bullet\sf{5x+3y=35}\\\bullet\sf{2x+4y=28}$

$\bf{\small{\red{\underline{\bf{To\:find\::}}}}}$

The value of x and y.

$\bf{\small{\red{\underline{\bf{Explanation\::}}}}}$

We know that formula of the cross multiplication method :

$\sf{\dfrac{x}{b_{1}c_{2}-b_{2}c_{1}} =\dfrac{y}{a_{2}c_{1}-a_{1}c_{2}} =\dfrac{1}{a_{1}b_{2}-a_{2}b_{1}}}$

So;

• 5x + 3y - 35 = 0
• 2x + 4y - 28 = 0

Therefore;

$\bullet\sf{a_{1}=5}\\\bullet\sf{a_{2}=2}\\\bullet\sf{b_{1}=3}\\\bullet\sf{b_{2}=4}\\\bullet\sf{c_{1}=-35}\\\bullet\sf{c_{2}=-28}$

A/q

$\mapsto\sf{\dfrac{x}{(3)(-28)-(4)(-35)} =\dfrac{y}{(2)(-35)-(5)(-28)} =\dfrac{1}{(5)(4)-(2)(3)}} \\\\\\\mapsto\sf{\dfrac{x}{-84+140} =\dfrac{y}{-70+140} =\dfrac{1}{20-6} }\\\\\\\mapsto\sf{\dfrac{x}{56} =\dfrac{y}{70} =\dfrac{1}{14} }\\\\\\\mapsto\sf{\dfrac{x}{56} =\dfrac{1}{14} \:\:Or\:\:\dfrac{y}{70} =\dfrac{1}{14} }\\\\\\\mapsto\sf{14x=56\:\:Or\:\:14y=70}\\\\\\\mapsto\sf{x=\cancel{\dfrac{56}{14}} \:\:\:Or\:\:\:y=\cancel{\dfrac{70}{14} }}\\\\\\\mapsto\sf{\red{x=4\:\:\:Or\:\:\:y=5}}$

Thus;

The value of x = 4 and y = 5 .

Answer 2

...

$\tt{\huge{\purple{ ................... }}}$

QUESTION -

solve the following by cross multiplication method :

1) 5x + 3y=35

2) 2x + 4y =28

SOLUTION :

Given Equations -

$5x + 3y = 35 .................. ( 1 ) \\ \\ 2x + 4y = 28 ............... ( 2 )$

$\dfrac{EQ_{1}}{EQ_{2} } => \dfrac{5x+3y}{2x+4y} = \dfrac{5}{4} \\ \\ => 5 ( 2x + 4y) = 4 ( 5x + 3y ) \\ \\ => 10x + 20y = 20 x + 12 y \\ \\ => 10x = 8y \\ \\ => 4y = 5x ......... ...... ( 3 )$

Substuting ( 3 ) in 2 -

$=> 7y = 28 \\ \\ => y = 4 ................ [ A _ { 1 } ]$

$=> 2x + 16 = 28 \\ \\ => 2x = 12 \\ \\ => x = 6 ................... [ A _ { 2 } ]$