Question

solve the following simultaneous equations: 4/x+3/y=1;6/x-15/y=8​

Answer 1

4x + 6/y=15...(i)

6x-8/y=14......(ii)

Multiply equation (i) by 'y' on both sides,

4xy + 6 = 15y

4xy - 15y = -6.....(iii)

Multiply equation (ii) by 'y' on both sides,

6xy - 8 = 14y

6xy - 14y = 8.......(iv)

Multiplying equation (iii) by 3 and (iv) by 2,

   12xy - 45y = -18

   12xy -28y = 16

-    (-)     (+)      (-)

-------------------------

            -17 y = - 34

Thus y = 2

Substituting y = 2 in equation (i),

    4x + 6/2 = 15

    4x = 12

Thus x = 3

Solved For x and y

Answer 2

$the \: equations \: are \\ \frac{4}{x} + \frac{3}{y} = 1 \\ \frac{6}{x} - \frac{15}{y} = 8 \\ \\ let \: \frac{1}{x} = a \: and\: \frac{1}{y} = b \: \: then \: the \: eqns \: will \: be... \\ 4a + 3b = 1 \\ 6a - 15b = 8 \\ \\ multiply \: the \: eqns \: by \: coefficients \: of \: \: a \: \: of \: one \: another.i.e. \\ (4a + 3b = 1) \times 6 \\ (6a - 15b = 8) \times 4 \\ \\ \: \: \: \: 24a + 18b = 6 \: \: \: \: eqn(1)\\ \: \: \: \: 24a - 60b = 32 \: \: \: eqn(2) \\\: \\ \: \: \: \: \: \: \: (2) - (1) \\ \\ 24a - 60b - 24a - 18b = 32 - 6 \\ - 78b = 26 \\ b = \frac{26}{ - 78} \\ b = \frac{ - 1}{3} \\ \\ put \: in \: eqn(1) \\ 24a + 18( \frac{ - 1}{3} ) = 6 \\ 24a - 6 = 6 \\ 24a = 6 + 6 = 12 \\ a = \frac{12}{24} \\ a = \frac{1}{2} \\ \\ answer \\ a = \frac{1}{2} \\ b = \frac{ - 1}{3}$

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