Consistent Pair of Linear Equations

Q.

Write the condition for a unique solution.

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.

If the system of equations: $kx+y+2z=1,3x-y-2z=2$ and $-2x-2y-4z=3$ has infinitely many solutions, then $k$ is equal to

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. The value of k for which the pair of linear equation 4x + 6y − 1 = 0 and 2x + ky − 7 = 0 represent parallel lines is

(a) k = 3

(b) k = 2

(c) k = 4

(d) k = −2

Q. Find the values of m and n for which the following system of linear equations has infinitely many solutions
$3x+4y=12(m+n)x+2(m-n)y=(5m-1)$

1. 
   4 and 1
2. 
   5 and 1
3. 
   5 and 2
4. 
   6 and 3

Q.

Describe Cauchy Riemann Equations

Q. If a pair of linear equations in two variables is consistent, then the lines represented by two equations are

(a) intersecting
(b) parallel
(c) always coincident
(d) intersecting or coincident

Q.

Given below are three equations. Two of them have infinite solutions and two have a unique solutions. state the two pairs.

$3x-2y=4,6x+2y=4,9x-6y=12$

Q.

On comparing the ratios, find out whether the lines representing the following pairs of linear equations at a point, are parallel or coincident:

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. consistent

2. dependent

3. inconsistent
4. (a) and (b) above.

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.

On comparing the ratios, find out whether the following pair of linear equations are consistent, or inconsistent.

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 = 4
4. k = 6

Q.

Question 4 (iii)
Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:
2x + y - 6 = 0, 4x - 2y - 4 = 0

Q. What is the easiest method to apply cross multiplication method?

Q. For what value of k, the following system of equations will represent the coincident lines?

x + 2y + 7 = 0
2x + ky + 14 = 0

Q. Question 1(ii)
Do the following pair of linear equations have no solution? Justify your answer.
x = 2y and y = 2x

Q. Question 1(ii)
Do the following pair of linear equations have no solution? Justify your answer.
x = 2y and y = 2x

Q. Condition for two lines to have a unique solution is,

1. $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
2. $\frac{a_1}{a_2}=\frac{b_1}{b_2}$
3. $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
4. $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Q. What is meant by consistent? What is meant by inconsistent?

Q.

Question 2 (iii)
On comparing the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
6x – 3y + 10 = 0
2x – y + 9 = 0

Q.

Question 1 (iii)
Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
3x - 5y = 20 ; 6x - 10y =40

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

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

Q. If a pair of linear equations is consistent, then their graph lines will be

(a) parallel
(b) always coincident
(c) always intersecting
(d) intersecting or coincident

Q.

Question 1 (i)
Do the following pair of linear equations have no solution? Justify your answer.
2x + 4y = 3 and 12y + 6x = 6

Q.

Question 1 (i)
Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
x - 3y - 3 = 0 ; 3x - 9y - 2 =0

Q. For what value of $K$ will the following pair of linear equations have infinitely many solutions?

Q. $3x+2y=5,2x-3y=7$ is an example of consistent pair of equations.

1. True
2. False

Q. The condition for which the equations $3x–2y=5\text{and}5x–ky=4$ are consistent with unique solution is

1. $k=\frac{10}{3}$
   
2. $k\ne \frac{10}{3}$
   
3. $k=\frac{-10}{3}$
   
4. $k\ne \frac{-10}{3}$