A) \[x-y=5\]
B) \[x+y=5\]
C) \[x+y=-\ 5\]
D) \[x-y=-\ 5\]
Correct Answer: B
Solution :
Point \[P(a,b)\]is on \[3x+2y=13\] So, \[3a+2b=13\] .....(i) Point \[Q(b,a)\]is on \[4x-y=5\] So, \[4b-a=5\] .....(ii) By solving (i) and (ii), \[a=3,b=2\] \[P(a,b)\to (3,\,2)\]and \[Q(b,a)\to (2,\,3)\] Now, equation of PQ \[y-{{y}_{1}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}(x-{{x}_{1}})\Rightarrow y-2=\frac{3-2}{2-3}(x-3)\] Þ \[y-2=-(x-3)\Rightarrow x+y=5\].
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