Maths-
General
Easy

Question

Solve the system of equation by using elimination: 2 over x plus 3 over y equals 1 text  and  end text 7 over x plus 4 over y equals 1 7 over 8

Hint:

Let  and 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 = 8 ; y = 4


    Ans :- x = 8 ; y = 4
    Explanation :-
    Let 1 over x equals a text  and  end text 1 over y equals b now we get the equation in a and b
    2 a plus 3 b equals 1— eq1
    7 a plus 4 b equals 15 divided by 8 — eq2
    Step 1 :- find value of b by eliminating a
    Do 2(eq2) - 7(eq1) to eliminate a
    2 left parenthesis 7 a plus 4 b right parenthesis minus 7 left parenthesis 2 a plus 3 b right parenthesis equals 15 divided by 4 minus 7 left parenthesis 1 right parenthesis
    14 a minus 14 a plus 8 b minus 21 b equals left parenthesis negative 13 divided by 4 right parenthesis not stretchy rightwards double arrow negative 13 b equals negative 13 divided by 4
    ∴ b = 1/4
    Step 2 :- find value of a by substituting b=1 in eq1
    2 a plus 3 b equals 1
    not stretchy rightwards double arrow 2 a plus 3 left parenthesis 1 divided by 4 right parenthesis equals 1 not stretchy rightwards double arrow 2 a equals 1 minus left parenthesis 3 divided by 4 right parenthesis
    not stretchy rightwards double arrow 2 a equals 1 divided by 4
    ∴ a = 1/8
    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 fraction numerator 1 over denominator 1 divided by 8 end fraction
    not stretchy rightwards double arrow x equals 8
     therefore space x space equals space 8
    y equals 1 divided by b not stretchy rightwards double arrow y equals fraction numerator 1 over denominator 1 divided by 4 end fraction
    not stretchy rightwards double arrow y equals 4
     therefore space y space equals space 4
    therefore x = 8 and y = 4 is the solution to the given pair of equations.

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