Question

Find the value of x and y in the below given pair of equation.

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

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

• A. 1/2, 1/3
• B. 1/3, 1/2
• C. 2, 3
• D. 3, 2

Answer 1

The correct option is A

1/2, 1/3

If we start solving the equation as it is, then we will find that after simplifying we will end up with two equations that are not linear.

2y+3x=13xy

5y-4x=-2xy

The above two equations are no longer linear equations.

So, to get the above equations in linear form we can substitute another variables instead of $\frac{1}{x}$ and $\frac{1}{y}$ .

So we will substitute $\frac{1}{x}$ as ‘a’ and $\frac{1}{y}$ as ‘b’

We will get our equations as

2a + 3b =13

5a - 4b = -2

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

Using the method of elimination

8a+12b = 52

15a-12b = -6

Now adding the two equations

23a = 46

$\Rightarrow$ a = 2

Now substitute the value of a in any of the two equations to obtain the value of b

b = 3

Earlier we have assumed that a= $\frac{1}{x}$

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

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