Question

solve equations 1 upon 2 x minus one upon Y is equal to -1 and 1 upon X + 1.2 equal to 8 where X is not equal to Y and Y is not equal to zero and X is not equal to

Answer 1

Answer:

$x=\frac{1}{6}\text{ and }y=\frac{1}{4}$

Step-by-step explanation:

Given equations,

$\frac{1}{2x}-\frac{1}{y}=-1$

$\frac{1}{x}+\frac{1}{2y}=8$

Where, x ≠ y and y ≠ x

Put A = 1/x and B = 1/y

Thus, the equations will be,

$\frac{A}{2}-B=-1$

$\implies A-2B = - 2-------(1)$

$A+\frac{B}{2}=8$

$\implies 2A+B=16---------(2)$

Equation (1) + 2 × Equation (2),

$A+4A=-2+32$

$5A=30$

$A=6$

From equation (1),

We get, B = 4,

Hence, x = 1/6 and y = 1/4,

Which is the solution of the given system of equations.

Answer 2

Answer:

$x=\frac{1}{6}\\y=\frac{1}{4}$

Step-by-step explanation:

$Given \: \frac{1}{2x}-\frac{1}{y}=-1\\and$

$\frac{1}{x}+\frac{1}{2y}=8$

$Let\: m=\frac{1}{x}\:and\:n=\frac{1}{y}$

Now , equations become,

$\frac{m}{2}-n=-1\\\implies \frac{m-2n}{2}=-1$

$\implies m-2n=-2\\\implies m = -2+2n\:---(1)$

$and\\m+\frac{n}{2}=8\:---(2)$

Now , substitute m = -2+2n in equation (2), we get

$-2+2n+\frac{n}{2}=8$

/* Multiply each term by 2 , we get

$\implies -4+4n+n=16$

$\implies 5n = 16+4$

$\implies n = \frac{20}{5}=4$

/* Substitute n=4 in equation (1) , we get

$m = -2+2\times 4\\\implies m = -2+8\\\implies m=6$

$Now,\\m =6=\frac{1}{x}$

$\implies x =\frac{1}{6}$

$Now,\\n =4=\frac{1}{y}$

$\implies y =\frac{1}{4}$

Therefore,

$x=\frac{1}{6}\\y=\frac{1}{4}$

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