A) \[x+y=7\]and\[4x+3y=24\]
B) \[x+y=24\]and\[4x+3y=7\]
C) \[x-y=7\]and\[4x-3y=24\]
D) None of the above
Correct Answer: A
Solution :
Let the intercepts of the line on the axes are \[a\] and\[b\], then equation of line is \[\frac{x}{a}+\frac{y}{b}=1\] ... (i) This line passes through\[(3,\,\,4)\] \[\therefore \] \[\frac{3}{a}+\frac{4}{b}=1\] ... (ii) Also, sum of the intercepts\[=14\] \[a+b=14\Rightarrow a=14-b\] Putting this value in Eq. (ii), we get \[\frac{3}{14-b}+\frac{4}{b}=1\] \[\Rightarrow \] \[3b+56-4b=15b-{{b}^{2}}\] \[\Rightarrow \] \[{{b}^{2}}-15b+56=0\] \[\Rightarrow \] \[{{b}^{2}}-8b-7b+56=0\] \[\Rightarrow \] \[b(b-8)-7(b-8)=0\] \[\Rightarrow \] \[(b-8)(b-7)=0\] \[\Rightarrow \] \[b=8,\,\,7\] If\[b=8\], then\[a=14-8=6\] If \[b=7\], then a =14-7= 7 Now, equation of line, if\[a=6,\,\,b=8\], is \[\frac{x}{6}+\frac{y}{8}=1\] \[\Rightarrow \] \[8x+6y=48\] \[\Rightarrow \] \[4x+3y=24\] and if\[a=7\], \[b=7\], then equation of line is \[\frac{x}{7}+\frac{y}{7}=1\Rightarrow x+y=7\]
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