Form the pair of linear equations for the following problem and find their solution by the substitution method.
The difference between two numbers is $26$ and one number is three times the other. Find the numbers.
The difference between two numbers is $26$ and one number is three times the other. Find the numbers.
(N/A) Let the first number be $x$ and the other number be $y$ such that $y > x$.
According to the given information:
$y = 3x$ $...(1)$
$y - x = 26$ $...(2)$
On substituting the value of $y$ from equation $(1)$ into equation $(2)$,we obtain:
$3x - x = 26$
$2x = 26$
$x = 13$ $...(3)$
Substituting the value of $x$ in equation $(1)$,we obtain:
$y = 3(13) = 39$
Hence,the two numbers are $13$ and $39$.
According to the given information:
$y = 3x$ $...(1)$
$y - x = 26$ $...(2)$
On substituting the value of $y$ from equation $(1)$ into equation $(2)$,we obtain:
$3x - x = 26$
$2x = 26$
$x = 13$ $...(3)$
Substituting the value of $x$ in equation $(1)$,we obtain:
$y = 3(13) = 39$
Hence,the two numbers are $13$ and $39$.
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