Question

1/3x-1/7y=2/3 1/2x-1/3y=1/6
Based on equations reducible to linear equation.​

Answer 1

Answer:

solution:

$x=\frac{1}{5}$

$y=\frac{1}{7}$

Step-by-step explanation:

$\frac{1}{3x}-\frac{1}{7y}=\frac{2}{3}$

$\frac{1}{2x}-\frac{1}{3y}=\frac{1}{6}$

The given equations can be written as

$\frac{1}{3}(\frac{1}{x})-\frac{1}{7}(\frac{1}{y})=\frac{2}{3}$

$\frac{1}{2}(\frac{1}{x})-\frac{1}{3}(\frac{1}{y})=\frac{1}{6}$

Take

$u=\frac{1}{x}$

$v=\frac{1}{y}$

we get

$\frac{1}{3}u-\frac{1}{7}v=\frac{2}{3}$

$\frac{1}{2}u-\frac{1}{3}v=\frac{1}{6}$

That is

7u - 3v =14

3u - 2v = 1

Now, we solve these equations by cross multiplication rule.

7u - 3v -14 =0

3u - 2v - 1 = 0

$\frac{u}{3-28}=\frac{v}{-42+7}=\frac{1}{-14+9}$

$\frac{u}{-25}=\frac{v}{--35}=\frac{1}{-5}$

$\frac{u}{-25}=\frac{1}{-5}$

$u=\frac{-25}{-5}$

$u=5$

$\frac{v}{--35}=\frac{1}{-5}$

$v=\frac{-35}{-5}$

$v=7$

$u=5$

implies $\frac{1}{x}=5$

$x=\frac{1}{5}$

$v=7$

implies $\frac{1}{y}=7$

$y=\frac{1}{7}$