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Maths / Linear Equations in Two Variables / Cross Multiplication Method
QUESTION
 

Solve the following system of equations using cross multiplication method : large frac{3x}{2}-frac{5y}{3}=-2 ;and; frac{x}{3}+frac{y}{2}=frac{13}{6}

OPTIONS
A. 

x = 2  , y = 3

B. 

x = -2  , y = 3

C. 

x = 2  , y = -3

D. 

x = -2  ,  y = 3

Right Option : A
EXPLANATION
Explain TypeExplanation Content
Text

large frac{3x}{2}-frac{5y}{3}=-2 ;and; frac{x}{3}+frac{y}{2}=frac{13}{6}

On comparing it with standard a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0,

a1 = 3/2 , b1 = -5/3 , c1 = 2 and a2 = 1/3, b2 = 1/2 , c2 = -13/6

x=frac{b1c2-b2c1}{a1b2-a2b1} and ; y=frac{c1a2-c2a1}{a1b2-a2b1}On substituting the values in x and y:

x=frac{(-5/3 times -13/6)-(1/2times 2)}{(3/2times 1/2)-(1/3 times -5/3)}=frac{65/18 - 1}{3/4 +5/9}=frac{47/18}{47/36}

x=frac{47}{18} times frac{36}{47}=2

y=frac{(2 times 1/3)-(-13/6 times 3/2)}{(3/2times 1/2)-(1/3 times -5/3)}=frac{2/3 +39/12}{3/4 +5/9}=frac{47/12}{47/36}

y=frac{47}{12} times frac{36}{47}=3

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