**Linear equations in two variables**

1) The linear equation 3x-11y=10 has:

a. Unique solution

b. Two solutions

c. Infinitely many solutions

d. No solutions

Answer: c

2) 3x+10 = 0 will have:

a. Unique solution

b. Two solutions

c. Infinitely many solutions

d. No solutions

Answer: a

3) The solution of equation x-2y = 4 is:

a. (0,2)

b. (2,0)

c. (4,0)

d. (1,1)

Answer: c

4) Find the value of k, if x = 1, y = 2 is a solution of the equation 2x + 3y = k.

a. 5

b. 6

c. 7

d. 8

Answer: d

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

a. 4/3

b. 5/3

c. 3

d. 7/3

Answer: b

6) The graph of linear equation x+2y = 2, cuts the y-axis at:

a. (2,0)

b. (0,2)

c. (0,1)

d. (1,1)

Answer: c

7) Any point on line x = y is of the form:

a. (k, -k)

b. (0, k)

c. (k, 0)

d. (k, k)

Answer: d

8) The graph of x = 3 is a line:

a. Parallel to the x-axis at a distance of 3 units from the origin

b. Parallel to the y-axis at a distance of 3 units from the origin

c. Makes an intercept 3 on the x-axis

d. Makes an intercept 3 on the y-axis

Answer: b

9) In equation, y = mx+c, m is:

a. Intercept

b. Slope

c. Solution of equation

d. None of the above

Answer: b

10) If x and y are both positive solutions of equation ax+by+c=0, always lie in the:

a. First quadrant

b. Second quadrant

c. Third quadrant

d. Fourth quadrant

Answer: a

11) A linear equation in two variables is of the form ax + by + c = 0, where

(a) a = 0, c = 0

(b) a ≠ 0, b = 0

(c) a = 0, b ≠ 0

(d) a ≠ 0, b ≠ 0

Answer: d

12) Any point on the x-axis is of the form

(a) (x, y)

(b) (0, y)

(c) (x, 0)

(d) (x, x)

Answer: c

13) Any point on the y-axis is of the form

(a) (y, y)

(b) (0, y)

(c) (x, y)

(d) (x, 0)

Answer: b

14) The linear equation 2x – 5y = 7 has

(a) No solution

(b) unique solution

(c) Two solutions

(d) Infinitely many solutions

Answer: d

15) The linear equation 3x – y = x – 1 has

(a) No solution

(b) unique solution

(c) Two solutions

(d) Infinitely many solutions

Answer: d

16) The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point

(a) (2, 0)

(b) (0, 2)

(c) (3, 0)

(d) (0, 3)

Answer: b

17) The equation 2x + 5y = 7 has a unique solution, if x, y are:

(a) Rational numbers

(b) Real numbers

(c) Natural numbers

(d) Positive real numbers

Answer: c

18) The point of the form (a, a) always lies on:

(a) On the line x + y = 0

(b) On the line y = x

(c) x-axis

(d) y-axis

Answer: b

19) If we multiply or divide both sides of a linear equation with the same non-zero number, then the solution of the linear equation:

(a) Remains the same

(b) Changes

(c) Changes in case of multiplication only

(d) Changes in case of division only

Answer: a

20) If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is

(a) 2

(b) 4

(c) 5

(d) 6

Answer: b

21) Which of the following is the equation of a line parallel to y-axis?

(a) y = 0

(b) x + y = z

(c) y = x

(d) x = a

Answer: (d) x = a

22) Any point of the form (a, – a) always lie on the graph of the equation

(a) x = -a

(b) y = a

(c) y = x

(d) x + y = 0

Answer: (d) x + y = 0

23) The graph of the equation 2x + 3y = 6 cuts the x-axis at the point

(a) (0, 3)

(b) (3, 0)

(c) (2, 0)

(d) (0, 2)

Answer: (b) (3, 0)

24) How many linear equations in x and y can be satisfied by x = 1 and y = 2?

(a) only one

(b) two

(c) infinitely many

(d) three

Answer: (c) infinitely many

25) Cost of book (x) exceeds twice the cost of pen (y) by Rs 10. This statement can be expressed as linear equation.

(a) x – 2y – 10 = 0

(b) 2x – y – 10 = 0

(c) 2x + y – 10 = 0

(d) x – 2y + 10 = 0

Answer: (a) x – 2y – 10 = 0

26) If x represents the age of father and y represents the present age of the son, then the statement for ‘present age of father is 5 more than 6 times the age of the son’ in terms of mathematical equation is

(a) 6x + y = 5

(b) x = 6y + 5

(c) x + 6y = 5

(d) x – 6 = 5

Answer: (b) x = 6y + 5

27) Equation of a line passing through origin is

(a) x + y = 1

(b) x = 2y – 4

(c) x + y = 0

(d) y = x – 1

Answer: (c) x + y = 0

28) The condition that the equation ax + by + c = 0 represents a linear equation in two variables is

(a) a ≠ 0, b = 0

(b) b ≠ 0, a = 0

(c) a = 0, b = 0

(d) a ≠ 0, b ≠ 0

Answer: (d) a ≠ 0, b ≠ 0

29) The maximum number of points that lie on the graph of a linear equation in two variables is.

(a) two

(b) definite

(c) infinitely many

(d) three

Answer: (c) infinitely many

30) Straight line passing through the points (-1, 1), (0, 0) and (1, -1) has equation

(a) y – x

(b) x + y = 0

(c) y = 2x

(d) 2 + 3y = 7x

Answer: (b) x + y = 0