Question

Form the pair of linear equations for the following problem and find their solution by substitution method.

The difference between the two numbers is $26$ and one number is three times the other. Find them.

Answer 1

Step 1: Assume variables and form the equations

Let, the first number $=x$

And, the second number $=y$

Here, $x>y$

Now, according to the question,

The difference between the two numbers $=26$

$\Rightarrow$ $x-y=26$ …(i)

Also, one number is three times the other, i.e.,

first number $=3\times$second number

$\Rightarrow$ $x=3y$ …(ii)

Step 2: Calculate $y$ by substitution

Substitute the value of $x$ in equation (i) from equation (ii),

$\because$ $x-y=26$

$\Rightarrow$ $3y-y=26$

$\Rightarrow$ $2y=26$

$\Rightarrow$ $y=\frac{26}{2}$

$\Rightarrow$ $y=13$

Step 3: Calculate $x$ by substitution

Substitute this value of $y$ in equation (ii),

$\because$ $x=3y$

$\Rightarrow$ $x=3\times 13$

$\Rightarrow$ $x=39$

So, the first number $=x=39$

And, the second number $=y=13$

Hence, the required numbers are $39$ and $13$.