A) \[3x-y=7\]and \[x+3y=9\]
B) \[x-3y=7\text{ }and\text{ }3x+y=9\]
C) \[x-y=3\,and\,x+y=2\]
D) \[2x+y=7\text{ }and\text{ }x-2y=9\]
E) \[2x-y=7\text{ }and\text{ }x+2y=9\]
Correct Answer: A
Solution :
The slope of line\[x-2y=3\] is \[\frac{1}{2}\]. Let the slope of required lines is m. \[\therefore \] \[\tan 45{}^\circ =\pm \left| \frac{\frac{1}{2}-m}{1+\frac{m}{2}} \right|\] \[\Rightarrow \] \[1+\frac{m}{2}=\pm \left( \frac{1}{2}-m \right)\] \[\Rightarrow \] \[-\frac{1}{2}=\frac{3m}{2}\Rightarrow m=\frac{-1}{3}\] Or \[1+\frac{m}{2}=\frac{-1}{2}+m\] \[\Rightarrow \] \[\frac{m}{2}=\frac{3}{2}\] \[\Rightarrow \]\[m=3\] \[\therefore \]Equation of line with slope\[m=\frac{1}{-3}\]and passing through (3, 2), is \[(y-2)=\frac{1}{-3}(x-3)\] \[\Rightarrow \] \[3y-6=-x+3\] \[\Rightarrow \] \[x+3y=9\] And another equation of line with slope\[m=3\]and passing through (3, 2), is \[(y-2)=3(x-3)\] \[\Rightarrow \] \[y-2=3x-9\] \[\Rightarrow \] \[3x-y=7\]
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