Pair of Linear Equations in Two Variables Set-2

Q1. For which value of $k$ does the system

have infinitely many solutions?

Q2. If $x$ and $y$ satisfy

then the value of $x^2+y^2$ is

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

have a solution $(x,y)$ such that $x+y=2$?

Q4. For which value of $k$ does the system

have no solution?

Q5. The lines

intersect at a point $(x,y)$. For which values of $k$ does this intersection lie on the circle $x^2+y^2=5$?

Q6. Solve the system of equations and find $(x,y)$:

Q7. For which value(s) of $k$ does the pair of linear equations have no solution?

Q8. A collection of Rs.2 coins and Rs.5 coins totals 30 coins and the amount is Rs.90. How many Rs.2 and Rs.5 coins are there respectively?

Q9. For which integer values of $k\;(k\neq 2)$ does the intersection point of the lines

have integer coordinates? (Here the second line is $kx+2y=6$.)

Q10. For what value(s) of $k$ does the solution $(x,y)$ of the system

satisfy $x+y=0$?

Q11. Solve the system

and find the value of $x+y$.

Q12. If

then find the value of $xy$.

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

Q14. For which value(s) of $k$ does the unique solution $(x,y)$ of the system

satisfy $x+y=1$?

Q15. For which value(s) of $k$ does the system

have product $xy=0$?