Role of Coefficients and Constants

Q.

If a pair of linear equations is consistent, then the lines are:

1. Parallel
2. Intersecting or coincident
3. Always intersecting
4. Always consistent

Q.

The pair of given lines $x+2y-4=0and2x+4y-12=0$ are ____

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

Q.

If twice the age of son is added to the age of father, the sum is 56. But if twice the age of the father is added to the age of son, the sum is 82. Find the ages of father and son.

1. Son = 10, Father = 36

2. Son = 10, Father = 16

3. Son = 10, Father = 26

4. Son = 8, Father = 36

Q.

Question 2
For which value(s) of k will the pair of equations
kx + 3y = k – 3,
12x + ky = k
has no solution?

Q.

Solve using cross multiplication method

2x + 3y = 17 and 3x - 2y = 6

1. (4, 3)

2. (3, 4)

3. (3, -4)

4. (-3, 4)

Q. Draw the graph of line X+y=5. Use the graph paper drawn to find the inclination and the y-intercept of the line.

Q. Question 4 (iii)
Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:
2x + y - 6 = 0, 4x - 2y - 4 = 0

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.

Solve using cross multiplication method

3x – 4y = 10 and 8x + 5y = 11

1. (2, 1)

2. (2, -1)

3. (-2, -1)

4. (-2, 1)

Q.

When a system of linear equations has no solution, what does it mean?

1. The lines are perpendicular

2. The lines intersect

3. The lines coincide

4. The lines are parallel

Q.

Find the Y intercept of the line 4x - 3y + 9 = 0. [2 MARKS]

Q. If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is .......

1. Consistent
2. Inconsistent
3. None of the Above
4. No solution

Q. Find the value of k for which following system of equations have infinitely many solutions
$2x+3y-5=0$
$6x+ky-15=0$

1. k = 9
2. k = 2
3. k = 3
4. k = 4

Q. Solve the equations: 2x+y=7 and 3x-y=3

1. x=2, y=3
2. x=3, y=4
3. x=5, y=3
4. x=2, y=6

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 are 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.

Solve

x + y = 2xy

x - y = 6xy

1. $x=\frac{-1}{2}andy=\frac{1}{4}$

2. $x=\frac{1}{2}andy=\frac{-1}{4}$

3. $x=\frac{1}{4}andy=\frac{-1}{4}$

4. $x=\frac{-1}{2}andy=\frac{-1}{2}$

Q. Find the value of $k$ for which following system of equations has a unique solution:
$x+2y=3$
$5x+ky+7=0$

Q.

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

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

2. none of these

3. The graph reaches infinity

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

Q.

Using properties of proportion, solve each of the following for $x$:

(iv) $\frac{\sqrt{12x+1}+\sqrt{2x-3}}{\sqrt{12x+1}-\sqrt{2x-3}}=\frac{3}{2}$.

Q.

Given graph represents _______________ pair of linear equations having _____________solution(s).

1. Dependent, infinite

2. None of these

3. Inconsistent , zero

4. Consistent, unique

Q.

For what value of k, will the following system of equations have infinitely many solutions?
$2x+3y=4,(k+2)x+6y=3k+2$

1. k = 2
2. k = 3
3. k = 4
4. k = 5

Q.

For what value of m, the system of equations $mx+3y=m–3,and12x+my=m$ will have no solution.

1. -4

2. -6

3. 4

4. 6

Q.

x - y = 0 is a line:

1. || to x axis

2. ||to y axis

3. Passing through origin

4. Passing through (1, -1)

Q.

x + 2y = 5 and 4x + 4y - 6 = 0 are two linear equations whose graphical lines meet at point (-2, 3.5). The pair of equations is:

1. Both A and B

2. Inconsistent

3. Dependent

4. Consistent

Q. Question 4 (iv)
Find the values of p for the following pair of equations 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.

Q. Question 4 (iii)
Find the value(s) of p for the following pair of equations – 3x + 5y = 7 and 2px – 3y = 1,
If the lines represented by these equations are intersecting at a unique point.

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.

Question 1 (i)
Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
x - 3y - 3 = 0 ; 3x - 9y - 2 =0

Q.

The condition for a pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ to be parallel is

1. ≠ = .

2. = ≠ .

3. = = .

4. ≠

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