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प्रश्न
Find the point of intersection of the following pairs of lines:
bx + ay = ab and ax + by = ab.
उत्तर
The equations of the lines are as follows:
bx + ay = ab
\[\Rightarrow\] bx + ay − ab = 0 ... (1)
ax + by = ab
\[\Rightarrow\] ax + by − ab = 0 ... (2)
Solving (1) and (2) using cross-multiplication method:
\[\frac{x}{- a^2 b + a b^2} = \frac{y}{- a^2 b + a b^2} = \frac{1}{b^2 - a^2}\]
\[ \Rightarrow \frac{x}{ab\left( b - a \right)} = \frac{y}{ab\left( b - a \right)} = \frac{1}{\left( a + b \right)\left( b - a \right)}\]
\[ \Rightarrow x = \frac{ab}{a + b} \text { and } y = \frac{ab}{a + b}\]
Hence, the point of intersection is \[\left( \frac{ab}{a + b}, \frac{ab}{a + b} \right)\].
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