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Linear Equation In Two Variable — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsLinear Equation In Two Variable2 Marks
Question
Very-Short and Short-Answer Questions:
The difference between two numbers is $5$ and the difference between their squares is $65$. Find the numbers.
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Answer

Let the number be $x$ and $y$, where $x > y.$
Then as per the question
$x - y = 5 ...(i)$
$x^2 - y^2 = 65 ...(ii)$
Dividing (ii) by (i), we get
$\frac{\text{x}^2-\text{y}^2}{\text{x}-\text{y}}=\frac{65}{5}$
$\Rightarrow\frac{(\text{x+y})(\text{x+y})}{\text{x}-\text{y}}=13$
$\text{x}+\text{y}=13\ ...(\text{iii})$
Now, adding (i) and (ii), we have
$2x = 18$
$\Rightarrow x = 9$
Substituting $x = 9$ in (iii), we have
$9 + y = 13$
$\Rightarrow y = 4$
$$Hence, the number are $9$ and $4.$

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