Question

3x/2-5y/3=-2,x/3+y/2=13/6 solve this by substitution method.
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Answer 1

Answer:

y=93/47

Step-by-step explanation:

Answer 2

SOLUTION :

We have two equation;

$\bullet\:\sf{\dfrac{3x}{2} -\dfrac{5y}{3} =-2......................(1)}\\\\\bullet\sf{\dfrac{x}{3} +\dfrac{y}{2} =\dfrac{13}{6} ..........................(2)}$

By substitution method :

From equation (1),we get;

$\longrightarrow\sf{\dfrac{3x}{2} -\dfrac{5y}{3} =-2}\\\\\\\longrightarrow\sf{\dfrac{9x-10y}{6} =-2}\\\\\\\longrightarrow\sf{9x-10y=-12}\\\\\\\longrightarrow\sf{9x=-12+10y}\\\\\\\longrightarrow\sf{x=\dfrac{-12+10y}{9} ....................(3)}$

Putting the value of x in equation (2),we get;

$\longrightarrow\sf{\dfrac{\dfrac{-12+10y}{9} }{3} +\dfrac{y}{2} =\dfrac{13}{6} }\\\\\\\longrightarrow\sf{\dfrac{-12+10y}{27} +\dfrac{y}{2} =\dfrac{13}{6}}\\\\\\\longrightarrow\sf{\dfrac{-24+20y+27y}{54} =\dfrac{13}{6} }\\\\\\\longrightarrow\sf{\dfrac{-24 +47y}{54} =\dfrac{13}{6} }\\\\\\\longrightarrow\sf{6(-24+47y)=13\times 54}\\\\\\\longrightarrow\sf{-144+282y=702}\\\\\\\longrightarrow\sf{282y=702+144}\\\\\\\longrightarrow\sf{282y=846}\\\\\\\longrightarrow\sf{y=\cancel{846/282}}$

$\longrightarrow\bf{y=3}$

Putting the value of y in equation (3),we get;

$\longrightarrow\sf{x=\dfrac{-12+10(3)}{9}}\\\\\\\longrightarrow\sf{x=\dfrac{-12+30}{9} }\\\\\\\longrightarrow\sf{x=\cancel{\dfrac{18}{9} }}\\\\\\\longrightarrow\bf{x=2}$

Thus;

The value of x & y will be 2 & 3 .