A) parallel
B) intersecting
C) coincident
D) None of the above
Correct Answer: B
Solution :
The given pair of linear equations is |
\[3x-5y+8=0\] |
and \[7x+6y-9=0\] |
On comparing the given equations with standard form of pair of linear equations i.e. |
\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] |
and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0,\]we get |
\[{{a}_{1}}=3,\,{{b}_{1}}=-5,\,{{c}_{1}}=8\] |
and \[{{a}_{2}}=7,\,{{b}_{2}}=6,\,{{c}_{2}}=-9\] |
Here, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{3}{7}\]and \[\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{-5}{6}\] |
\[\because \,\,\,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\] |
\[\therefore \] The lines representing the given pair of linear equations will intersect at a point. |
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