Consistency and Inconsistency of Linear Equations in Two Variables

Q.

The value of $\text{k}$ for which the system of equations $\text{x+2y-3=0}$ and $\text{5x+ky+7=0}$ has no solution, is

Q.

Question 1 (ii)
For which value(s) of $\lambda$ does the pair of linear equations $\lambda x+y={\lambda }^{2}andx+\lambda y=1$ have infinitely many solutions?

Q. If a pair of lines do not intersect at a point, then find the number of solutions.

1. A unique solution
2. Infinitely many solutions
3. No Solution
4. None of the above

Q.

If the given pair of equations has infinitely many solutions, then find the value of $k$ ?

$2x+4y=k$

$6x+12y=9$

1. $1$
2. $2$
3. $3$
4. $4$

Q. How many solutions does the given system of equations has/have?

$3x+4y=25$
$15x+20y=35$

1. A unique solution.
2. Infinitely many solutions
3. No solution
4. None of the above

Q.

What is the solution of the equation: $5x+10y=35?$

1. $(1,3)$

2. $(3,2)$

3. $(5,1)$

4. Infinite pair of values of $x$ and $y$

Q. Question 1 (ii)
For which value (s) $\lambda$, do the pair of linear equations $\lambda x+y={\lambda }^{2}andx+\lambda y=1$ have infinitely many solution.

Q. Question 1 (iii)
For which value (s) $\lambda$, do the pair of linear equations $\lambda x+y={\lambda }^{2}andx+\lambda y=1$ have a unique solution?

Q. If the pair of linear equations
$3x+2y=1$
$(2k+1)x+(k+2)y=k-1$
Has infinitely many solution, then the value of k is

1. 2
2. 4
3. 3
4. 5

Q.

In the figure, ∠ POR and ∠QOR form a linear pair. If a – b = 70^o the values of a and b are

1. a = 130^o, b = 50^o

2. a = 105^o, b = 75^o

3. a = 135^o. b = 45^o

4. a = 125^o, b = 55^o

Q. The linear pairs of equations $\left(3k+1\right)x+3y-5=0and2x-3y+5=0$ have infinite solutions. Find the value of $K.$

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

Q. Find the number which when multiplied by 7 is increased by 78.

Q. For which values of 'a' and 'b' does the following pair of linear equations have infinite number of solutions -
$2x+3y=7,(a-b)x+(a+b)y=3a+b-2$

1. $a=4,b=2$
2. $a=5,b=1$
3. $a=1,b=5$
4. $a=2,b=4$

Q.

What is the solution of the equation: $5x+10y=35?$

1. $(1,3)$

2. $(3,2)$

3. $(5,1)$

4. Infinite pair of values of $x$ and $y$

Q. How many solutions does the given system of equations has/have?

$3x+4y=7$
$15x+20y=35$

1. A unique solution
2. Infinitely many solutions
3. No solution
4. None of the above

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. S1 and S2

2. S1 only

3. S1 and S3

4. S2 only

Q. The system of equations $x+2y=3$ and $3x+6y=9$ has

1. Unique solution
2. No solution
3. Infinitely many solutions
4. Finite number of solutions

Q. In which of the following situations does solutions of right angles not apply?

1. Racing tracks
2. Finding the distance of stars from sun
3. Wheelchair ramps
4. Finding the size of micro-organisms

Q. For what values of $a$ does each of the following system of equations have an infinite number of solutions?
$(a-2)x+27y=4.5,2x+(a+1)y=-1$

Q. Find the value of a and b for which the given system of linear equations has an infinite number of solutions.

1. $a=2,b=-9$
2. $a=7,b=-13$
3. $a=0,b=4$
4. $a=5,b=1$

Q. What can one observe about a solution to the given lines?

1. A solution is not possible as the lines do not intersect.
2. When the lines are extended further they will intersect and point of intersection will be the solution.
3. The lines will coincide and will have infinite solutions.
4. The lines are parallel and hence no solution is possible.

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. 6
4. 4

Q. Select the pair of equations that are consistent.

1. x+y=1, 2x+2y=2
2. 3x+3y=3, 2x+2y=2
3. 4x+4y=4, 2x+2y=2
4. x+y=1, 2x+2y=4
5. 5x+5y=5, 2x+2y=2
6. 6x+6y=6, 2x+2y=2
7. x+y=1, 7x+7y=7
8. x+y=8, 2x+2y=2

Q. What is the solution for the two lines given in the graph?

1. x = -9, y = -3
2. x = 9, y = -3
3. x = -3, y = 9
4. x = -3, y = -9

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

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

Q.

For which value(s) of λ do the pair of linear equations λx + y = λ² and x + λy = 1 have infinitely many solutions ?

1. 0 and 1
2. 0
3. 1
4. 0 and -1