Q1. The pair of equations $x = 0$ and $x = 5$ has:
Q2. If the lines given by $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel, then the value of $k$ is:
Q3. The value of $c$ for which the pair of equations $cx - y = 2$ and $6x - 2y = 4$ will have infinitely many solutions is:
Q4. Assertion (A): The lines represented by $2x + 3y = 9$ and $4x + 6y = 18$ are coincident. Reason (R): If $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$, then the lines are coincident.
Q5. Check whether the pair of equations $x - 2y = 0$ and $3x + 4y = 20$ is consistent or inconsistent.
Solve on white paper.
Q6. For what value of $k$ does the pair of linear equations $x + 2y = 3$ and $5x + ky + 7 = 0$ have a unique solution?
Q7. Find the value of $k$ for which the system of equations $3x + y = 1$ and $(2k-1)x + (k-1)y = 2k+1$ has no solution.
Q8. Find the values of $a$ and $b$ for which the following pair of linear equations has infinitely many solutions: $2x + 3y = 7$ $(a-b)x + (a+b)y = 3a + b - 2$.
Q9. Determine the nature of the lines representing the paths given by equations $2x - 3y = 8$ and $4x - 6y = 9$. Do the paths cross each other?
Q10. Solve the following system of equations graphically: $2x + y = 6$ $2x - y + 2 = 0$ Shade the region bounded by these lines and the x-axis. Find the coordinates of the vertices of the triangle so formed.
Q11. Case Study: Railway Tracks
Two railway tracks are represented by the equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$.
(i) Compare the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$.
(ii) Geometrically, what do these lines represent? Will the tracks ever meet?
(iii) If the second track was represented by $2x + 4y - 8 = 0$, what would be the nature of the two tracks?