Chapter 4: Linear Equations in two Variables

Choose the correct answers :

Q1. The linear equation  has :

(A) A unique solution    (B) Two solutions          (C) Infinitely many solutions    (D) No solution

Answer: (C) Infinitely many solutions   . 

Q2. A linear equation in two variables is of the form  , where

(A)       (B)     (C)     (D)

Answer:  (A)       .

Q3. Any point on the y -axis is of the form

(A) (x,0)       (B) (x,y)      (C) (0,y)        (D) (y,0)

Answer: (C) (0 , y).      

Q4. If (2,0) is a solution of the linear equation  then the value of k is :

(A) 4            (B) 6            (C) 5      (D) 2

Ans:  (A)  4

[Hints:  Here , x=2 , y=0

  2x+3y=k

 ⇒2×2+3×0=k

 ⇒4=k

⇒k=4  ]

Q5. 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)

Ans: (D) (0,2)

[Hints:  Here , x=0

  2x+3y=6

 ⇒2×0+3×y=6

 ⇒3y=6

⇒y=2  ]

Q6. x=5 , y=2 is a solution of the linear equation

(A) x+2y=7        (B)  5x+2y=7     (C)  x+y=7     (D) 5x+y=7

Ans:  (C)  x+y=7     .

[Hints:  Given,  x=5 , y=2

 x+y=7  

L.H.S. :   5+2=7  R.H.S. ]

Q7. If a linear equation has solution -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

Ans: (B)  x+y=0     .

[Hints: x+y=0

⇒x=-y 

                                        ]

Q8. 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)

Ans :   (C)  (3,0)

[ Hints: y=0 

2x+3y=6 

⇒2x+3×0=6 

⇒2x=6 

⇒x=3     ]