Solutions of Simultaneous Linear Equations

Q. Consider the simultaneous linear equations
$3x+4y=1$
And, $9x+12y=3$.
How many solutions does this system of equations have?

1. No solution
2. Infinitely many solution
3. Unique solution
4. Two solution

Q. Find the number of solutions of simultaneous linear equations:
$9y=15x+3$
$6y=10x+4$

1. No solution
2. Infinitely many solution
3. Unique solution
4. None of the above

Q. Consider set of linear equations :$4x+7y=p$ and $kx+28y=120$, Where $k$ and $p$ are constant number. If these equation are having Infinitely many solution. Then, What will be the value of $k$ and $p$?

1. $k=16$
2. $p=30$
3. $k=30$
4. $p=16$

Q. A system of two linear equations
$y+3x=-3$
$2y=cx+d$
has no solutions. Then, find the value of $c$ and $d$

1. $c\ne -6$, $d\ne -6$
2. $c=-6$, $d\ne -6$
3. $c\ne -6$, $d=-6$
4. $c=-6$, $d=-6$

Q. Consider the system of simultaneous linear equation:
$y+ax=b$
$x+3y=10$
Where $a$ and $b$ are constants.
Which of the following possible values of $a$ and $b$ makes the equation having no solution.

1. $a=\frac{1}{3}$ and $b=2$
2. $a=\frac{1}{3}$ and $b=\frac{10}{3}$
3. $a=\frac{1}{3}$ and $b=6$
4. None of the above.

Q. Does the following pair of linear equations have a unique solution?
$7x+2y=21$
$21x+6y=63$

1. yes
2. no

Q. Choose the correct statement related to simultaneous linear equations:

1. If two simultaneous linear equations while plotting on cartesian coordinate intersect each other, then the equations have no solution.
2. If two simultaneous linear equations have infinitely many solution, they will overlap while plotting on cartesian plane.
3. When two lines are parallel to each other, their simultaneous linear equations have Unique solution.
4. If two simultaneous linear equations while plotting on cartesian coordinate intersect each other, then the equations have unique solution.

Q. The system of linear equations is given as
$y+2x=4$
$2y+4y=6$
Which of the following is the solution to the above system?

1. $(2,1)$
2. $(1,1)$
3. $(-1,1)$
4. $\text{No solution}$

Q. Does the following pair of linear equations have a unique solution?
$2x+\frac{y}{2}=3$
$y=2x$

1. yes
2. no

Q. Line $1$: $4x+2y=6$ and Line $2$: $y=px+q$ have infinite number of solutions, then $p$ and $q$ are

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

Q. Does the following pair of linear equations have a unique solution?
$2x+3y=6$
$y=\left(\frac{-2}{3}\right)x+\frac{5}{6}$

1. yes
2. no

Q. For what value of $a$, the lines $2x+3y=3$ and $ax+12y=12$ will have an infinite number of solutions?

1. $8$
2. $-8$
3. $4$
4. $-4$