Nature of Solutions of a Pair of Linear Equations

If $kx + my + 4 = 0 \text{and} 2x+y+1 = 0$ the two equations are inconsistent, what is $k:m$?

Find the value of $k$ for which the system of equation will have a many solution

$2x+ky=1$

$3x-3y=7$

Find the value of $k$ for which the system of equation will have a No solution

$2x+ky=1$

$3x-3y=7$

Find the value of $k$ for which the system of equation will have a unique solution

$2x+ky=1$

$3x-3y=7$

Check whether the following pair of equations is consistent.

$$\begin{gathered} 3x+4y-2=0 \\ 6x+8y-4=0 \end{gathered}$$

For what value of $p$, the system of equations $2x+3y-14= 0$and $5x-py-14=0$ will not have a unique solution?

Write a pair of linear equations in $2$ variables which have infinite solutions.

If a pair of linear equations given by $a_{1}x+b_{1}y+c_1=0 \text{and} a_{2}x+b_{2}y+c_2=0$ has a unique solution, then which of the following is true$?$

Shown below is a pair of linear equations.

$mx+4y-6= 0$

$ny-12x+12= 0$

For which of the following values of $m \text{and }n$ do the above equations have infinitely many solutions?

Find the value of $\alpha$ so that the following linear equations have no solution.

$\left(3\alpha +1\right)x+3y-2= 0, \left({\alpha }^2+1\right)x+\left(\alpha -2\right)y-5= 0$

Find the value of $k$ for which the given system of equations has a unique solution and infinitely many solutions.

$$\begin{gathered} kx+2y=5 \\ 3x+y=2.5 \end{gathered}$$

If $am=bl$, then find whether the pair of equations $ax+by=c$ and $lx+my=n$ has no solution, unique solution or infinitely many solution$?$

Show that for each real value of $\lambda$, the system of equations $\left(\lambda +3\right)x+\lambda y=0, x+\left(2\lambda +5\right)y=0$ has a unique solution.

On comparing $\frac{a_1}{a_2}, \frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$,  find whether the given pair of equations parallel or not.

$6x-3y+10=0, 2x-y+9=0$

On comparing $\frac{a_1}{a_2}, \frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$,  find whether the given pair of equation intersect at a point or not.

$5x-4y+8=0, 7x+6y-9=0$

For what value of $p$ will the system of equations $3x + y = 1, (2p – 1)x + (p – 1) y = (2p + 1)$ has no solution 

Which of the following pair of equation has no solution.

For what value of $p$ will the following pair of linear equations have infinitely many solutions. 
$$\begin{gathered} (p-3)x+3y=p \\ px+py=12 \end{gathered}$$

A pair of linear equation has infinite many solutions if

The pair of linear equations $x+2y=5,7x+3y=13$has a unique solution if