Solution of a Pair of Linear Equations

Q. Point (3, 4) lies on the graph of the equation 𝟑𝒚 = 𝒌𝒙 + 𝟕. The value of 𝒌 is:

1. 5/3
2. 4/3
3. 3
4. 7/3

Q.

In the system of equations above, $a$ is a constant. For $-3x+y=6;ax+2y=4$
Which of the following values of $a$ does the system have no solution?

1. $-6$

2. $-3$

3. $3$

4. $6$

Q. Parallel lines have no solution.

1. False
2. True

Q.

The distance between the points (4, 8) and (k, -2) is 10. Find the value of k

1. 3

2. 4

3. 6

4. 10

Q.

Choose the correct statements.

1. Equation of AC is 2y = x

2. Equation of BD is y=x-2

3. The point of intersection of the lines is ( 4, 2)

4. All the above

Q.

The graph for the following system of equations :

$2x+3y=5$ and $6x+9y=40$ is shown

$S_1:\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

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. Point (3, 4) lies on the graph of the equation 𝟑𝒚 = 𝒌𝒙 + 𝟕. The value of 𝒌 is:

1. 5/3
2. 4/3
3. 3
4. 7/3

Q.

What is the point that lies on x = 5 and has ordinate as -3 ?

1. (-5, 3)
2. (-5, -3)
3. (5, -3)
4. (5, 3)

Q.

The x and y intercepts of the line 2x + 3y =12 are

1. 6, 4

2. 12 , -2/3

3. -2/3 , 12

4. 4, 6

Q.

The x and y intercepts of the line 2x + 3y =12 are respectively

1. 4, 6

2. -2/3 , 12

3. 6, 4

4. 12 , -2/3

Q. If the point P(8, a) lies on the line $\frac{x}{4}+\frac{y}{5}=1$, then find the value of a .........[2 marks]

Q.

Find the X and Y intercepts of 3x + 5y = 15

Q. The pair of equations $x=0$ and $y=-7$ has

1. One solution
2. Two solutions
3. Infinitely many solutions
4. No solution

Q.

Choose the correct statement

1. Equation of AC is 2y = x

2. Equation of BD is y=3x-2

3. The point of intersection of the lines is ( 4, 2)

4. All the above

Q.

The x-intercept of the line 3y = 12 is

1. 12, -2/3

2. -2/3 , 12

3. 6, 4

4. 4, 6

Q.

What is the solution for the two lines in the given graph?

1. (0, 0)

2. (4, 2)

3. (-5, 2)

4. (5, 2)

Q.

Condition satisfied by the pair of equation $2x+3y=-5$ and $4x+6y-10=0$ is

1. = =

2. = ≠

3. ≠

4. ≠ = .

Q.

The x-intercept of the line 3y = 12 is

1. 4, 6

2. -2/3 , 12

3. 6, 4

4. 12, -2/3

Q.

Find the X and Y intercepts of:
(a) x + 3y = 12
(b) 3x + 5y = 15 [4 MARKS]

Q. Match the following type of lines with their number of solutions.

1. Infinite
2. One
3. Zero

Q.

What is the solution for the two lines in the given graph?

1. (5, 2)

2. (0, 0)

3. (4, 2)

4. (-5, 2)

Q. Match the following type of lines with their number of solutions.

1. One
2. Infinite
3. Zero

Q. Match the following columns:

Column I	Column II
(a) Any line parallel to the x-axis is	(p) 3
(b) Any line parallel to the y-axis is	(q) y = mx
(c) Any line passing through the origin is	(r) x = k
(d) If the point (−2, 2) lies on the line ax + 4y = 2, then a =	(s) y = k

(a) ......,
(b) ......,
(c) ......,
(d) ......,

Q. Match the following columns:

Column I	Column II
(a) The equation of a line parallel to the x-axis is	(p) y = mx
(b) The equation of a line parallel to the y-axis is	(q) $\frac{5}{2}$
(c) The equation of a line through the origin is	(r) x = k
(d) If the point (2, 3) lies on the graph of the equation 3y = ax + 4, then a =	(s) y = k

(a) ......,
(b) ......,
(c) ......,
(d) ......,

Q.

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

Q. Find the intersection of each of the following pairs of sets.
(i) A = {1, 2, 4, 5, 7}, B = {2, 3, 4, 8}
(ii) C = {x|x $\in$ N, 5 < x $\le$10} D = {y|y $\in$ W, 5 $\le$ y < 10}
(iii) E = {x|x $\in$I, x < 0} F = {y|y $\in$ I, Y > 0}

Q.

The x and y intercepts of the line 2y = 3x

1. ¹/₂ and ¹/₃

2. 2 and 3

3. 3 and 2

4. 0 and 0

Q. On drawing the graphs of the linear equations $4x-3y+4=0$ and $4x+3y-20=0$ the area bounded by this line and $x$ axis is

1. $10sq$ units
2. $12sq$ units
3. $5sq$ units
4. $6sq$ units