4. Linear Equations in two Variables Class 9 Mathematics NCERT Exemplar Solutions (CBSE)
Chapter 4: Linear Equations in two Variables – Class 9 Mathematics NCERT Exemplar Solutions (CBSE Board)
Chapter 4: Linear Equations in two Variables
EXERCISE 4.1
Write the correct answer in each of the following :
1. The linear equation 2x – 5y = 7
has
(A) A unique solution (B) Two solutions
(C) Infinitely many solutions (D) No solution
2. The equation 2x + 5y = 7
has a unique solution, if x, y
are :
(A) Natural numbers (B) Positive real numbers
(C) Real numbers (D) Rational numbers
3. If (2, 0) is a solution of the linear equation 2x + 3y = k
, then the value of k
is
(A) 4 (B) 6 (C) 5 (D) 2
4. Any solution of the linear equation 2x+ 0y + 9 = 0
in two variables is of the form
(A) (– 92
, m) (B) (n, – 92 ) (C) (0, – 92 ) (D) (– 9, 0)
5. The graph of the linear equation 2x + 3y = 6
cuts the y-axis at the point
(A) (2, 0) (B) (0, 3) (C) (3, 0) (D) (0, 2)
6. The equation = 7
, in two variables, can be written as
(A) 1 . x + 1 . y = 7
(B) 1. x + 0. y = 7
(C) 0 . x + 1 . y = 7
(D) 0 . x + 0 . y = 7
7. Any point on the x
-axis is of the form
(A) (x, y) (B) (0, y
) (C) (x, 0) (D) (x, x
)
8. Any point on the line y = x
is of the form
(A) (a, a
) (B) (0, a
) (C) (a, 0
) (D) (a, – a
)
9. The equation of x-axis is of the form
(A) x = 0
(B) y = 0
(C) x + y = 0
(D) x = y
10. The graph of y = 6
is a line
(A) parallel to x-axis at a distance 6 units from the origin
(B) parallel to y-axis at a distance 6 units from the origin
(C) making an intercept 6 on the x-axis.
(D) making an intercept 6 on both the axes.
11. x = 5, y = 2
is a solution of the linear equation
(A) x + 2 y = 7
(B) 5x + 2y = 7
(C) x + y = 7
(D) 5 x + y = 7
12. If a linear equation has solutions (–2, 2), (0, 0) and (2, – 2), then it is of the form
(A) y – x = 0
(B) x + y = 0
(C) –2x + y = 0
(D) –x + 2y = 0
13. The positive solutions of the equation ax + by + c = 0
always lie in the
(A) 1st quadrant (B) 2nd quadrant
(C) 3rd quadrant (D) 4th quadrant
14. The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point
(A) (0, 2) (B) (2, 0) (C) (3, 0) (D) (0, 3)
15. The graph of the linear equation y = x passes through the point
(A) ( 32 , -32
) (B) ( 0 ,32
) (C) (1, 1) (D) ( -12 , 12 
)
16. If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation :
(A) Changes
(B) Remains the same
(C) Changes in case of multiplication only
(D) Changes in case of division only
17. 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
18. The point of the form (a, a) always lies on :
(A) x-axis (B) y-axis
(C) On the line y = x (D) On the line x + y = 0
19. The point of the form (a, – a) always lies on the line
(A) x = a
(B) y = – a
(C) y = x (D) x + y = 0
6. If the point (3, 4) lies on the graph of 3y = ax + 7, then find the value of a.
9. For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution.
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