Question

Find value of x,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

In the above given pair of equations we see that the variables are in form of and . If we start solving the equation as it is then we will find that after simplifying we will end up in two equations that are not linear.

See what we will get

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 equation by using any of the three methods (elimination, substitution and cross multiplication) to solve the pair of linear equation.

If we use method of elimination

First equation can be written as

8a+12b = 52

15a-12b = -6

Now adding the two equations

23a=46

→ a=2

Now substitute the value of a in any of the two equations and we will find out the value of b

b=3

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

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

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