Maths-
General
Easy

Question

Solve: fraction numerator 1 over denominator 2 x end fraction plus fraction numerator 1 over denominator 3 y end fraction equals 2 and fraction numerator 1 over denominator 3 x end fraction plus fraction numerator 1 over denominator 2 y end fraction equals 13 over 6 by using elimination method.

Hint:

Let 1 over x equals a and 1 over y equals b now we get the equation in a and b
Now find values of a and b .After finding a and b substitute them in and and find the values of x and y .

The correct answer is: x=1/2 ; y=1/3


    Ans :- x = 1/2 ; y = 1/3
    Explanation :-
    Let 1 over x equals a and 1 over y equals b now we get the equation in a and b
    a over 2 plus b over 3 equals 2 — eq1
    a over 3 plus b over 2 equals 13 over 6 — eq2
    Step 1 :- find value of b by eliminating a
    Do 3(eq2) - 2(eq1) to eliminate a
    3 open parentheses a over 3 plus b over 2 close parentheses minus 2 open parentheses a over 2 plus b over 3 close parentheses equals 3 left parenthesis 13 divided by 6 right parenthesis minus 2 left parenthesis 2 right parenthesis
    a minus a plus fraction numerator 3 b over denominator 2 end fraction minus fraction numerator 2 b over denominator 3 end fraction equals left parenthesis 13 divided by 2 right parenthesis minus 4 not stretchy rightwards double arrow fraction numerator 5 b over denominator 6 end fraction equals 5 over 2
    ∴ b = 6/2 = 3
    Step 2 :- find value of a by substituting b=1 in eq1
    a over 2 plus b over 3 equals 2 not stretchy rightwards double arrow a over 2 plus 3 over 3 equals 2
    a over 2 equals 2 minus 1 not stretchy rightwards double arrow a equals 2
    ∴ a = 2
    Step 3 :-  substitute a and b  in 1 over x equals a text  and  end text 1 over y equals b and find values of x and y
    x equals 1 divided by a not stretchy rightwards double arrow x equals 1 half
     therefore space x space equals space 1 half
    y equals 1 divided by b not stretchy rightwards double arrow y equals 1 third
     therefore space y space equals space 1 third
    therefore space x space equals space 1 divided by 2 spaceand y = 1/3 is the solution to the given pair of equations.

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