Consistent pair of LE

Q.

Explain Consistent and Inconsistent Systems and its representation.

Q.

Find the value of k for which the system of equations
$6x+7y=0,kx+21y=0$ has infinitely many solutions.

____

Q. Find the values of k for which the following system of equations have infinitely many solutions.
(i) 2x + 3y = 7
(ii) (k + 2)x + (2k + 1)y = 3(2k - 1)

1. 8
2. 2
3. 4
4. 6

Q. For the equation $y=mx+b$, if y and x are proportionally related to each other, then

Q.

The lines that represent these two equations $x+2y=5$ and $4x+4y-6=0$ meet at only one point (-2, 3.5). The pair of equations is

1. inconsistent
2. (a) and (b) above.

3. dependent

4. consistent

Q. The pair of linear equations $13x+ky=k$ and $39x+6y=k+4$ has infinitely many solutions if:

1. k = 1
2. k = 2
3. k = 6
4. k = 4

Q.

The value of a for which the lines $x=1$, $y=2$ and $a^{2}x+2y-20=0$ are concurrent is:

1. 1
2. 4
3. -1
4. -2

Q. Which of these pairs of lines are consistent?

1. x = 2; 2x - 7y - 5 = 0
2. 3y - 2x = 2; 2x - 3y = 2
3. $\frac{x}{3}+\frac{y}{2}=1;x+\frac{3y}{2}=1$
   
4. $\sqrt{3}x-y=2;\sqrt{6}x-\sqrt{2}y=2$

Q. Which of the following equations are consistent?

1. $2x+4y=11;2x+4y=23$
2. $7x-y=5;14x-2y=4$
3. $x+y=7;2x-y=8$
4. $x-y=5;2x-2y=11$

Q. If a pair of linear equations is consistent, then the lines are:

1. Always consistent
2. Always intersecting
3. Intersecting or coincident
4. Parallel

Q.

What do we call a system of equations that don't have a solution?

1. Inconsistent

2. Consistent

3. Independent

4. Coincident