The Straight Lines — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines3 Marks
Question
Find the point of intersection of the following pairs of lines: bx + ay = ab and ax + by = ab.
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Answer
$\text{bx+ay}=\text{ab}\Rightarrow\text{x}=\frac{\text{ab}-{\text{ay}}}{b}$ Putting this value in the second equation, we get $\text{ax} + \text{by} = \text{ab}$ $\text{a}\Big(\frac{\text{ab}-\text{ay}}{b}\Big)+\text{by}=\text{ab}$ $\text{a}^2\text{b}-\text{a}^2\text{y}+\text{b}^2\text{y}=\text{a}\text{b}^2$ $\text{y}(\text{b}^2-\text{a}^2)=\text{ab}(\text{b}-\text{a})$ $\text{y}=\frac{\text{ab(b-a)}}{\text{b}^2-\text{a}^2}=\frac{\text{ab}}{\text{b+a}}$ Putting this value in the first equation, we get $\Rightarrow\text{x}=\frac{\text{ab}-\frac{\text{a(ab)}}{\text{a+b}}}{\text{b}}=\frac{\text{ab}}{\text{a+b}}$ $\therefore$ point is $\Big(\frac{\text{ab}}{\text{a+b}},\frac{\text{ab}}{\text{a+b}}\Big)$
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