Neha Tyagi and Amit Rastogi Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 2: Exercise

Do the following equations represent a pair of coincident lines? Justify your Answer.

$\frac{x}{2}+y+\frac{2}{5}=0$ and $4x+8y+\frac{5}{16}=0$

Are the following pair of linear equations consistent? Justify your answer.

$-3x-4y=12$ and $4y+3x=12$

Are the following pair of linear equations consistent? Justify your answer.

$\frac{3}{5}x-y=\frac{1}{2}$ and $\frac{1}{5}x-3y=\frac{1}{6}$

Are the following pair of linear equations consistent? Justify your answer.

$2ax+by=a$ and $4ax+2by-2a=0;a,b\ne 0$

Are the following pair of linear equations consistent? Justify your answer.

$x+3y=11$ and $2\left(2x+6y\right)=22$

For the pair of equations $\lambda x+3y+7=0$ and $2x+6y-14=0$. To have infinitely many solutions, the value of $\lambda$ should be $1$. Is the statement true? Give reasons.

For all real values of $c$, the pair of equations $x-2y=8$ and $5x-10y=c$ have a unique solution. Justify whether it is true or false.

The line represented by $x=7$ is parallel to the $X-$axis, justify whether the statement is true or not.