Question

$\frac{4}{x} + \frac{5}{y} = 7 \:; \: \frac{3}{x} + \frac{4}{y} = 5$
SOLVE HCCVGYBGHUFGG​

Answer 1

Explanation:

\Large\mathtt{\frac{ \frac{x}{4} - \frac{3}{5} }{ \frac{4}{3 } - 7x} = \frac{ - 3}{20}}

3

4

−7x

4

x

−

5

3

=

20

−3

First take the L.C.M of the denominators of the fractions in the numerator of the bigger fraction

L.C.M of 4 and 5 is 20

As 5 is a prime number and whenever we have to find the L.C.M of two numbers and one of them is prime, we simply multiply those numbers

4 × 5 = 20, so the L.C.M is 20

Now we have to multiply the denominators with a number to make it 20

We will multiply 4 with 5 to make it 20

And multiply 5 with 4 to make it 20

Now, when we multiply the denominators with a number we also have to multiply the numerators also with the same number, so

\begin{gathered}\Large\mathtt{\frac{ \frac{x}{4} \times \frac{5}{5} - \frac{3}{5} \times \frac{4}{4} }{ \frac{4}{3 } - 7x} = \frac{ - 3}{20}} \\ \\ \\ \implies\Large\mathtt{\frac{ \frac{5x}{20} - \frac{12}{20} }{ \frac{4}{3 } - 7x} = \frac{ - 3}{20}} \\ \\ \\ \implies\Large\mathtt{\frac{ \frac{5x - 12}{20} }{ \frac{4}{3 } - 7x} = \frac{ - 3}{20}}\end{gathered}

3

4

−7x

4

x

×

5

5

−

5

3

×

4

4

=

20

−3

⟹

3

4

−7x

20

5x

−

20

12

=

20

−3

⟹

3

4

−7x

20

5x−12

=

20

−3

Now, take the L.C.M of the denominators of the fractions in the denominator of the bigger fraction

When there is nothing in the numerator like in 7x

We take the numerator as 1 :

\Large\mathtt{\frac{ \frac{x}{4} - \frac{3}{5} }{ \frac{4}{3 } - \frac{7x}{1} } = \frac{ - 3}{20}}

3

4

−

1

7x

4

x

−

5

3

=

20

−3