Inconsistent pair of LE

Q.

For which value(s) of $k$ will the pair of equations $kx+3y=k-3$ and $12x+ky=k$ have no solution?

Q.

Match the following:
$\begin{array}{cc}\text{A. y}=-\frac{3}{2}-\frac{x}{2};\text{x= -3 -2y}& \text{(i) Inconsistent pair}\\ \text{B. 5x = 6-3y; 9y= 12-15x}& \text{(ii) Dependent pair}\\ \text{C. y}=\frac{2}{7}-\frac{x}{7};\text{y}=\frac{18}{5}-\frac{x}{5}& \text{(iii) Unique solution}\end{array}$

1. A-i, B-iii, C-ii

2. A-ii, B-i, C-iii

3. A-ii, B-iii, C-i

4. A-iii, B-i, C-ii

Q.

Which of the following pairs of linear equations is inconsistent?
$1.x+3y–5=0,2x+y=0$
$2.2x+y=1,2y=2–4x$
$3.2x–y=2,2y–4x=2$

1. $x+3y–5=0,2x+y=0$

2. $2x+y=1,2y=2–4x$

3. $2x–y=2,2y–4x=2$

4. All of the above.

Q. Which of the following pairs of equations is inconsistent?

1. $4x+y=12;8x+2y=24$
2. $x+2y=5;2x+4y=15$
3. $2x+3y=15;4x+7y=11$
4. $11y+3x=1;5y+2x=7$

Q.

In the pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Statement 1 : This is an inconsistent pair of linear equations.

Statement 2 : There exists infinitely many solutions.

Statement 3 : The lines representing these linese are parallel.

Which of the above statements is/are true?

1. S2 only

2. S1 and S2

3. S1 and S3

4. S1 only

Q. If the two lines are parallel and do not intersect, then the system of equations is ____.

1. inconsistent with one solution
2. consistent with one solution
3. consistent with many solutions
4. inconsistent with no solution

Q.

Given graph represents _______________ pair of linear equation having _____________solution(s).

1. Consistent, unique

2. Inconsistent , zero

3. Dependent, infinite

4. None of these

Q.

When a system of linear equations has no solution, what does it mean?

1. The lines are parallel.

2. The lines are perpendicular to each other.

3. The lines intersect at a point.

4. The lines coincide.