# Linear equations in two variables

## 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

2) 3x+10 = 0 will have:

a. Unique solution

b. Two solutions

c. Infinitely many solutions

d. No solutions

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

a. (0,2)

b. (2,0)

c. (4,0)

d. (1,1)

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

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

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)

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

a. (k, -k)

b. (0, k)

c. (k, 0)

d. (k, k)

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

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

a. Intercept

b. Slope

c. Solution of equation

d. None of the above

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

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

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

(a) (x, y)

(b) (0, y)

(c) (x, 0)

(d) (x, x)

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

(a) (y, y)

(b) (0, y)

(c) (x, y)

(d) (x, 0)

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

(a) No solution

(b) unique solution

(c) Two solutions

(d) Infinitely many solutions

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

(a) No solution

(b) unique solution

(c) Two solutions

(d) Infinitely many solutions

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)

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

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

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

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

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

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)

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

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

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