Assertion Reasoning Quiz

Assertion (A): The value of \(k\) for which the system of linear equations \(3 x-4 y=7\) and \(6 x-8 y=k\) have infinite number of solution is 14.
Reason (R): The graph of linear equations \(a_1 x+b_1 y+c_1=0\) and \(a_2 x+b_2 y+c_2=0\) gives a pair of intersecting lines if \(\frac{a 1}{a 2} \neq \frac{b 1}{b 2}\).

Assertion (A) : The value of p for which the system of equations \(4 \mathrm{x}+\mathrm{py}+8=0\) and \(2 \mathrm{x}+2 \mathrm{y}+2=0\) is consistent is 4.

Reason (R) : The system of equations \(\mathrm{a}_1 \mathrm{x}+\mathrm{b}_1 \mathrm{y}=\mathrm{c}_1\) and \(\mathrm{a}_2 \mathrm{x}+\mathrm{b}_2 \mathrm{y}=\mathrm{c}_2\) is consistent with infinitely many solutions, if \(\frac{\mathrm{a}_1}{\mathrm{a}_2}=\frac{\mathrm{b}_1}{\mathrm{~b}_2}=\frac{\mathrm{c}_1}{\mathrm{c}_2}\).

Assertion (A): The substitution method can be used to solve a pair of linear equations.
Reason (R): In substitution, one variable is expressed in terms of the other.

Assertion (A): The area of the trapezium formed by the lines \(3 x+4 y-12=\) 0 and \(3 x+4 y=6\) is \(\frac{9}{2}\) square units.
Reason (R): The system of equations \(a_1 x+b_1 y+c_1=0\) and \(a_2 x+b_2 y+ c_2=0\) is inconsistent, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\).

Assertion (A): There are infinite number of lines which passes through (3, 2).
Reason (R): A linear equation in two variables has infinitely many solutions.