10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

On comparing the ratios \[{{a}_{1}}/{{a}_{2}},\,{{b}_{1}}/{{b}_{2}}\]and \[{{c}_{1}}/{{c}_{2}}\]and without drawing them, the pair of linear equation is \[3x-5y+8=0,7x+6y-9=0\]

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.