Comparing the ratios of coefficients of LE

Q.

A rational number becomes $\frac{1}{3}$ on subtracting $1$ from its numerator and it becomes $\frac{1}{4}$when $8$ is added to its denominator, the rational number is:

1. $\frac{5}{12}$

2. $\frac{1}{12}$

3. $\frac{7}{12}$

4. $\frac{7}{17}$

Q. Find the value of $k$ for which the given system of equations has infinite number of solutions.

1. 4
2. 7
3. 3
4. 6

Q. The graphical representation of the pair of equations
$x+2y-4=0and2x+4y-12=0$ is?

1. Intersecting lines
2. Parallel lines
3. Coincident lines
4. All of these

Q. Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions.
(i) $x-3y-3=0;3x-9y-2=0$

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. Both A and B.

2. none of these

3. These represent coincident lines

4. The system of equations have infinite solutions

Q.

For what value of m, the system of equations $mx+3y=m–3,12x+my=m$ will have no solution.

1. -4

2. 4

3. -6

4. 6

Q. $\frac{x}{2}+\frac{y}{3}=4;\frac{x}{4}+\frac{y}{6}=2$

1. no solution
2. Infinite solutions
3. unique solution
4. Cannot be determined

Q.

How do you determine the value(s) of $k$ such that the system of linear equations $4x+ky=6$ and $kx+y=-3$ has an infinite number of solutions?

Q. Which of the following pairs of linear equations has unique solution , or infinity many solutions . In case there is a unique solution , find it by using cross multiplication method .
$x-3y-3=0$
$3x-9y-2=0$