Comparing the ratios of coefficients of LE

Q.

Do the following equations represent a pair of coincident lines? Justify your answer.

$3x+\frac{1}{7}y=3$

$7x+3y=7$

Q.

If one of the lines given by $6x^2-xy+4c{y}^2=0$ is $3x+4y=0$, then $c$ equals

1. $-3$

2. $-1$

3. $3$

4. $1$

Q. Determine the value of k for which the given system of equations has a unique solution:
$x-ky=2,3x+2y=-5$

1. The given system of equations will have unique solution for all real values of k other than
2. The given system of equations will have unique solution for all real values of k other than
3. The given system of equations will have unique solution for all real values of k other than
4. The given system of equations will have unique solution for all real values of k other than

Q.

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

1. The graph reaches infinity

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

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

4. none of these

Q.

If one of the lines given by $6x^2-xy+4c{y}^2=0$ is $3x+4y=0$, then $c$ equals

1. $-3$

2. $-1$

3. $3$

4. $1$

Q.

Parallel lines are obtained for the pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ if

1. ≠ = .

2. = ≠ .

3. = = .

4. ≠

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 false and S2 is true

2. S1 is true and S2 is false

3. S1 and S2 are true

4. S1 and S2 is false

Q.

The condition for $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ to be consistent and have a unique solution is

1. $\frac{a_1}{a_2}$ = $\frac{b_1}{b_2}$ = $\frac{c_1}{c_2}$

2. $\frac{a_1}{a_2}$ ≠​ $\frac{b_1}{b_2}$

3. $\frac{a_1}{a_2}$ = $\frac{b_1}{b_2}$ ≠ $\frac{c_1}{c_2}$

4. $\frac{a_1}{a_2}$ =​ $\frac{b_2}{b_1}$ = $\frac{c_1}{c_2}$

Q.

For what value of k, the pair of linear equations $3x+ky=9$ and $6x+4y=18$ has infinitely many solutions?

1. -5

2. 6

3. 1

4. 2

Q.

When 6 is added to the numerator of a fraction, the numerator becomes twice the denominator. In another fraction, 10 times the denominator exceeds 5 times the numerator by 30. The number of solutions for the given equations is

1. 1

2. 0

3. Infinitely many solutions

4. 2

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. No solution

3. Infinite solutions

4. Two solutions

Q.

If $a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0$ are two equations with infinite solutions , then
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

1. True

2. False

Q. Father's present age is $x$. If his son is 30 years younger than him, then the son's present age is $x-30$.

1. True
2. False

Q.

If $a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0$ are two equations with an unique solution, then
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

1. True

2. False

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.

The graph for the following system of equations :

$2x+3y=5and6x+9y=40$ is shown

S1: $\frac{a_1}{a_2}$= $\frac{b_1}{b_2}$ ≠ $\frac{c_1}{c_2}$

S2 : The two lines intersect each other.

1. S1 is true but S2 is false

2. S1 is false but S2 is true

3. S1 and S2 are true

4. S1 and S2 are false

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.

What can you say about the ratio of the coefficients for the lines $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ from the graph ?

1. a₁/a₂ ≠ b₁/b₂ = c₁/c₂

2. a₁/a₂ = b₁/b₂ = c₁/c₂

3. a₁/a₂ ≠ b₁/b₂

4. a₁/a₂ = b₁/b₂ ≠ c₁/c₂

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

Q. Which of these pairs of lines are parallel?

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

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. 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. Father's present age is $x$. If his son is 30 years younger than him, then the son's present age is $x-30$.

1. True
2. False