Pair of Linear Equations in Two Variables Set-1

Q1. For which value of $k$ does the following pair of linear equations have infinitely many solutions?

Q2. The lines represented by the equations

intersect at a point which lies on the line $x+2y=3$. The value of $k$ is

Q3. For which value of $k$ does the system

have a solution with $x=y$?

Q4. Find all real values of $m$ for which the system

has no solution.

Q5. For which integer values of $k$ does the system

admit an integer solution $(x,y)$?

Q6. For the pair of equations

the system will have infinitely many solutions for which value of $k$?

Q7. For which values of $k$ does the system

have a unique solution?

Q8. The lines $x+2y=3$ and $2x-y=a$ meet at a point which lies on the circle $x^2+y^2=5$. The possible values of $a$ are:

Q9. Consider the system

For which value of $k$ is the system inconsistent (i.e., has no solution)?

Q10. For which value of $k$ does the solution of the system

satisfy $x+y=1$?

Q11. Solve the system of equations

and choose the correct ordered pair $(x,y)$.

Q12. A shopkeeper sold two kinds of notebooks, one priced at ₹25 and the other at ₹15. He sold a total of 50 notebooks and received ₹1100. Let $x$ be the number of ₹25 notebooks and $y$ the number of ₹15 notebooks. Which pair $(x,y)$ satisfies the situation?

Q13. For which value(s) of $k$ does the following system have no solution?

Q14. For which real value(s) of $k$ does the solution of the system

lie on the line $x+y=1$?

Q15. Let $k$ be a real number and consider the system

For which $k$ are both components of the solution $(x,y)$ non-negative?