Simultaneous Linear Equations

Q. If a pair of lines intersect at a point, then find the number of solutions.

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

Q. If a pair of lines are coincident, then find the number of solutions.

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

Q. Which of the following pairs of equations have the same solutions?

1. 6x = 3 and 3x = 1.5
2. 8x = 3 and 4x = 1
3. 10x = 9 and 5x = 18
4. 12x = 6 and 6x = 6

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

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

1. 3
2. 4
3. 5
4. 7

Q. Find the value of $k$ for which each of the following systems of equations have infinitely many solution:
$2x+3y=2$
$(k+2)x+(2k+1)y=2(k-1)$

Q. A unique solution?

Q. In the following given systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it
$3x-5y=20$
$6x-10y=40$

Q. Find the next term in the following series :

4, 2, 7, 5, 10, 8, __, __

1. 13, 11
2. 12, 10
3. 14, 16
4. 16, 18

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

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

Q. lines do not intersect each other.

1. Non parallel
2. Parallel
3. Coincident

Q.

Find the values of $a$ and $b$ for which the following system of linear equations has infinite number of solutions?

$2x+3y=7;(a+b+1)x+(a+2b+2)y=4(a+b)+1$