Question

Solve for x and y by the method of cross multiplication: 4x – 3y –1 = 0 ; 5x – 7y = –2

Answer 1

${\underline{\underline{\red{\sf{Given:}}}}}$

• A linear equation in two variable.
• To solve for x & y .

${\underline{\underline{\red{\sf{To\:Find}}}}}$

• Value of x and y .
• We have to solve by cross multiplication method.

${\underline{\underline{\red{\sf{Concept\:Used}}}}}$

• We will use the formula of 'Method of Cross-multiplication ' for finding the values of x and y .

${\underline{\underline{\red{\sf{Answer:}}}}}$

We have been given two linear equations which are

• $\sf{4x-3y-1=0}$
• $\sf{5x-7y+2=0}$

$\sf{\pink{With\:respect\:to\:Standard\:Form}}$

$\sf{ a_{1}=4\:\:\:\:\:\:\:b_{1}=(-3)\:\:\:\:\:\:\:c_{1}=(-1)}$

$\sf{ a_{2}=5\:\:\:\:\:\:\:b_{2}=(-7)\:\:\:\:\:\:\:c_{2}=(2)}$

${\underline{\purple{\sf{The\:formula\:is\: stated\:as}}}}$

$\large\red{\boxed{\blue{\bf{\dfrac{x}{(b_{1}c_{2}-b_{2}c_{1})}=\dfrac{y}{c_{1}a_{2}-c_{2}a_{1}}=\dfrac{1}{a_{1}b_{2}-a_{2}b_{1}}}}}}$

$\sf{\green{On\: putting\: the\:values}}$

$\sf{\implies \dfrac{x}{(-3\times2)-(-1\times-7)}=\dfrac{y}{(4\times2)-(5\times(-1))}=\dfrac{1}{(7\times(-4))-(-5\times3)}}$

$\sf{\implies \dfrac{x}{-6-7}=\dfrac{y}{8+5}=\dfrac{1}{-28+15}}$

$\sf{\implies \dfrac{x}{-13}=\dfrac{y}{13}=\dfrac{1}{-13}}$

$\sf{\implies \dfrac{x}{-13}=\dfrac{1}{-13}}$

${\underline{\boxed{\orange{\sf{\mapsto x =1}}}}}$

$\sf{\dfrac{y}{13}=\dfrac{1}{-13}}$

${\underline{\boxed{\orange{\sf{\mapsto y =-1}}}}}$

Therefore ,

• x =1
• y=(-1)