R S Aggarwal and Veena Aggarwal Solutions for Exercise 6: Exercise 3F

For what value of $\mathrm{k}$ does the following pair of linear equations have infinitely many solutions?

$10\mathrm{x}+5\mathrm{y}-(\mathrm{k}-5)=0, 20\mathrm{x}+10\mathrm{y}-\mathrm{k}=0$

For what value of $\mathrm{k}$ will the following pair of linear equations have no solution?

$2\mathrm{x}+3\mathrm{y}=9, 6\mathrm{x}+(\mathrm{k}-2) \mathrm{y}=(3\mathrm{k}-2)$

If the value of $\mathrm{k}\ne \mathrm{a}$ for which the system of equations $3\mathrm{x}+\mathrm{ky}=0, 2\mathrm{x}-\mathrm{y}=0$ has a unique solution, then find the value of $\mathrm{a}$.

The difference between two numbers is $5$ and the difference between their square is $65$. Find the smallest number.

Find the value of $k$ for which the system $3x+5y=0$ and $kx+10y=0$ has a non-zero solution.

Find $k$ for which the system $2x+3y-5=0$ and $4x+ky–10=0$ has an infinite number of solutions.

Show that the system $2x+3y-1=0$ and $4x+6y-4=0$ has no solution.

Find $k$ for which the system $x+2y–3=0$ and $5x+ky+7=0$ is inconsistent.