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Pair of Linear Equations in Two variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two variables5 Marks
Question
Solve the following pairs of equations:
$\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=\text{a}+\text{b},\frac{\text{x}}{\text{a}^2}+\frac{\text{y}}{\text{b}^2}=2\text{ a},\text{ b}\neq0$
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Answer

Given pair of linear equations is
$\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=\text{a}+\text{b}\ .....(\text{i})$ and $\frac{\text{x}}{\text{a}^2}+\frac{\text{y}}{\text{b}^2}=2\text{ a},\text{ b}\neq0\ .....\text{(ii)}$
On multiplying Eq. (i) by $\frac{1}{\text{a}}$ and then subtracting from Eq. (ii),
we get

$\Rightarrow\ \text{y}\Big(\frac{\text{a}-\text{b}}{\text{ab}^2}\Big)=1-\frac{\text{b}}{\text{a}}=\Big(\frac{\text{a}-\text{b}}{\text{a}}\Big)$
$\Rightarrow\ \text{y}=\frac{\text{ab}^2}{a}\Rightarrow\ \text{y}=\text{b}^2$
Now, put the value of y in Eq. (ii),
we get $\frac{\text{x}}{\text{a}^2}+\frac{\text{y}}{\text{b}^2}=2$
$\Rightarrow\ \frac{\text{x}}{\text{a}^2}=2-1=1$
$\Rightarrow\ \text{x}=\text{a}^2$
Hence, the required values of x and y are $a^2$ and $b^2$​​​​​​​,respectively.

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