Comparing the Ratios of Coefficients of a Linear Equation

Q. Given pair of linear equation in the graph intersect each other.

Q. Which of these pairs of lines are parallel?

1. 3y - 2x = 2; 3x - 2y = 2
2. $\sqrt{3}x-y=2;\sqrt{6}x-\sqrt{2}y=2$
3. $\frac{x}{3}+\frac{y}{2}=1;x+\frac{3y}{2}=3$
4. y = 3; 2x - 7y - 5 = 0

Q. Coincident lines have infinite solutions. Which among the following pairs of lines are coincident?

1. $x-y=1$ ; $x+y=1$
2. $3x=5+2y$ ; $y=4x+1$
3. $x=\frac{11}{5}-\frac{2y}{5};y=\frac{11}{2}-\frac{5x}{2}$
4. $x-y=2$ ; $x+y=2$

Q. The pair of linear equations $2x+5y=-11and5x+15y=-44$ have

1. No solutions
2. One solutions
3. Two solutions
4. Many solutions

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. only (a) and (b)

4. none of these

Q.

A unique solution for a pair of linear equations is obtained if

S1 : the graphs of the equations have only one point of intersection.

S2 : The ratio of coefficients of the two variables is equal.

1. S1 is true and S2 is false

2. S1 is false and S2 is true

3. S1 and S2 are true

4. S1 and S2 is false

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

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

Q.

The reason for the equations $x+2y=5$ and $4x+8y=20$ to have infinite solutions is

1. The graph of the system of equations meets at infinity

2. The graph reaches infinity

3. The graph of both the equations is the same line

4. none of these

Q.

For a pair of linear equations
$a_{1}x+b_1+c_1=0$ and $a_{2}x+b_2+c_2=0$
$a_1=12,b_1=2,c_1=6$ and $a_2=24,b_2=4,c_2=7$.
Find the number of solutions the pair of equations will have.

1. One solution

2. Infinite solutions

3. Two solutions

4. No solution

Q.

The system of pair 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