Question

Solve the given pair of equations.

$\frac{2}{x}$ + $\frac{3}{y}$ = 13

$\frac{5}{x}$ - $\frac{4}{y}$ = -2

• A. $\frac{1}{2}$, $\frac{1}{3}$
• B. $\frac{1}{3}$, $\frac{1}{2}$
• C. 2, 3
• D. 3, 2

Answer 1

The correct option is A

$\frac{1}{2}$, $\frac{1}{3}$

Given

$\frac{2}{x}$ + $\frac{3}{y}$ = 13

$\frac{5}{x}$ - $\frac{4}{y}$ = -2

Substitute $\frac{1}{x}$ as ‘a’ and $\frac{1}{y}$ as ‘b’

The equations reduces to

$2a+3b=13$

$5a-4b=-2$

Now we can solve this pair of equation by using any of the three methods (elimination, substitution and cross multiplication).

If we use method of elimination

Multiply the first equation by 4 and second by 3. Equations can be written as

$8a+12b=52$

$15a-12b=-6$

Now adding the two equations

$23a=46$

$\Rightarrow a=2$

Substitute the value of a in any of the two equations to get b.

$\Rightarrow b=3$

Since $a=\frac{1}{x}$

Therefore $x=\frac{1}{2}$

Similarly $y=\frac{1}{3}$