Solve the following pair of simultaneous equations-1-x - 1-y - 50ex0ex1-x - 1-y - 1

We have:1/x + 1/y = 50ex0ex1/x 1/y = 1Let 1/x = u and 1/y = vu + v = 50ex0exu – v = 1On adding both equations, 2u = 6 and u = 3Put u = 3 in one of the equatio ...

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Standard X

Mathematics

Elimination Method of Finding Solution of a Pair of Linear Equations

Solve the fol...

Question

Solve the following pair of simultaneous equations:
$\frac{1}{x} + \frac{1}{y} = 5 \frac{1}{x} - \frac{1}{y} = 1$

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Solution

We have:
$\frac{1}{x} + \frac{1}{y} = 5 \frac{1}{x} - \frac{1}{y} = 1$
Let $\frac{1}{x} = u$ and $\frac{1}{y} = v$
$u + v = 5 u - v = 1$
On adding both equations, $2 u = 6$ and $u = 3$
Put $u = 3$ in one of the equations to get the value of $v$ to be $2$ .
Now,
$\frac{1}{x} = 3$ and $\frac{1}{y} = 2$
Hence, $x = \frac{1}{3}$ and $y = \frac{1}{2}$ are the solution of given pair of equation.

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Δ = ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{(1 + a_{1} b_{1}) (1 + a_{1}^{2} b_{1}^{2} - a_{1} b_{1})}{1 + a_{1} b_{1}} & \frac{(1 + a_{1} b_{2}) (1 + a_{1}^{2} b_{2}^{2} - a_{1} b_{2})}{1 + a_{1} b_{2}} & \frac{(1 + a_{1} b_{3}) (1 + a_{1}^{2} b_{3}^{2} - a_{1} b_{3})}{1 + a_{1} b_{3}} \frac{(1 + a_{2} b_{1}) (1 + a_{2}^{2} b_{1}^{2} - a_{2} b_{1})}{1 + a_{2} b_{1}} & \frac{(1 + a_{2} b_{2}) (1 + a_{2}^{2} b_{2}^{2} - a_{2} b_{2})}{1 + a_{2} b_{2}} & \frac{(1 + a_{2} b_{3}) (1 + a_{2}^{2} b_{3}^{2} - a_{2} b_{3})}{1 + a_{2} b_{3}} \frac{(1 + a_{3} b_{1}) (1 + a_{3}^{2} b_{1}^{2} - a_{3} b_{1})}{1 + a_{3} b_{1}} & \frac{(1 + a_{3} b_{2}) (1 + a_{2}^{2} b_{2}^{2} - a_{3} b_{2})}{1 + a_{3} b_{2}} & \frac{(1 + a_{3} b_{3}) (1 + a_{3}^{2} b_{3}^{2} - a_{3} b_{3})}{1 + a_{3} b_{3}} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣

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Solve the following pair of simultaneous equations:1x+1y=51x-1y=1

We have:1x+1y=51x-1y=1Let 1x=u and 1y=vu+v=5u–v=1On adding both equations, 2u=6 and u=3Put u=3 in one of the equations to get the value of v to be 2.Now,1x=3 and 1y=2Hence, x=13 and y=12 are the solution of given pair of equation.

Solve the following pair of simultaneous equations:
$\frac{1}{x} + \frac{1}{y} = 5 \frac{1}{x} - \frac{1}{y} = 1$