Classification of Pair of Linear Equations

Q. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

Q.

To which of the following types the straight lines represented by $2x+3y-7=0$ and $2x+3y-5=0$ belong?

1. Parallel to each other

2. Perpendicular to each other

3. Inclined at $45°$ to each other

4. Coincident pair of straight lines

Q. Question 2 (ii)
Do the following equations represent a pair of coincident lines? Justify your answer.
– 2x – 3y = 1 and 6y + 4x = - 2

Q. Question 2 (iii)
Do the following equations represent a pair of coincident lines? Justify your answer.
$\frac{x}{2}+y+\frac{2}{5}=0and4x+8y+\frac{5}{16}=0$

Q.

Question 3 (iv)
Are the following pair of linear equations consistent? Justify your answer
x + 3y = 11 and 2(2x + 6y) = 22

Q. $3x+2y=6\&6x+4y=18$ are ______.

1. parallel lines
2. coincident lines
3. dependent pair of linear equations
4. intersecting lines

Q.

Question 2 (i)
Do the following equations represent a pair of coincident lines? Justify your answer.
$3x+\frac{1}{7}y=3and7x+3y=7$

Q.

Question 2 (i)
Do the following equations represent a pair of coincident lines? Justify your answer.
$3x+\frac{1}{7}y=3and7x+3y=7$

Q.

Question 3 (iv)
Are the following pair of linear equations consistent? Justify your answer
x + 3y = 11 and 2(2x + 6y) = 22

Q.

In the question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion(A): The solution of the pair of linear equations $3x-4y=7$ and $6x-8y=k$ have infinite number of solution if $k=14$.

Reason(R): $a_1+b_{1}y+c_1=0$ and $a_2+b_{2}y+c_2=0$ have a unique solution if $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$.

1. Both the assertion (A) and the reason (R) are true, but the reason (R) is not the correct explanation of assertion (A).​

2. The assertion (A) is false, but the reason (R) is true.​

3. The assertion (A) is true, but the reason (R) is false.​

4. Both the assertion (A) and the reason (R) are true, and ​the reason (R) is the correct explanation of the assertion (A).​

Q. $x+y=30$ and are coincident lines.

1. $4x+5y=150$
2. $5x+5y=150$
3. $5x+5y=15$

Q. $y=2x+4$ and are parallel lines.

1. $2y=4x+8$
2. $y=2$
3. $y=2x-3$

Q. Question 9
One equation of a pair of dependent linear equations is - 5x + 7y – 2 = 0
(A) 10x + 14y + 4 = 0
(B) –10x – 14y + 4 = 0
(C) –10x + 14y + 4 = 0
(D) 10x – 14y = –4​​​​​​​

Q. Match the following type of lines with their number of solutions.

1. One
2. Infinite
3. Zero

Q.

If $D=0$ and at least one of $D_1,D_2,D_3$ is not 0 then according to Cramer's rule the system of linear equations will have

1. trivial solution

2. infinite solutions

3. no solutions

4. non trivial solution

Q. By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.
$x+y=3$ and $3x+3y=9$

Q. Find the consistent pair of linear equations from the following.

1. $x+2y=42x+4y=8$
2. $2x+y=-43x-2y=8$
3. $2x+3y=42x+3y=8$
4. $4x+6y=42x+3y=8$

Q. Find the dependent pair of linear equations from the following.

1. $x+2y=42x+4y=8$
2. $x+3y=4x+4y=15$
3. $3x+2y=82x+3y=12$
4. $x+4y=102x+2y=6$

Q.

The system of equations 4x -3y +12 =0 and 2x +3y -15 =0 has

1. a unique solution

2. infinitely many solutions

3. no solution

4. 2 solutions

Q.

What is a consistent linear system?

Q. Question 2 (iii)
Do the following equations represent a pair of coincident lines? Justify your answer.
$\frac{x}{2}+y+\frac{2}{5}=0and4x+8y+\frac{5}{16}=0$

Q.

Question 2 (i)
Do the following equations represent a pair of coincident lines? Justify your answer.
$3x+\frac{1}{7}y=3and7x+3y=7$

Q. Find the value of k for which the given system of equations has no solution?
$x+2y=3$
$3x+ky-15=0$

1. $k\ne 6$
2. $k\ne 7$
3. $k=6$
4. None of the above

Q. $2x+3y=1\&3x-y=7$ are ______.

1. intersecting lines
2. parallel lines
3. coincident lines
4. dependent pair of linear equations

Q.

If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ for the system of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$

1. These represent coincident lines

2. The system of equations have infinite solutions

3. Both A and B.

4. none of these

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. Find the inconsistent pair of linear equations from the following.

1. $x+2y=42x+4y=4$
2. $2x+y=-43x-2y=8$
3. $2x+y=42x+3y=8$
4. $4x+3y=82x+6y=16$

Q. The pair of linear equations $3x-5y+1=0,2x-y+3=0$ has a unique solution $x=x_1,y=y_1$ then $y_1=$

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

Q.

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

1. Inconsistent

2. Consistent

3. Independent

4. Coincident

Q. Intersecting lines are consistent.

1. False
2. True