Assignment 9th Class Topic:- Linear equation in two variable CBSE/NCERT (For CPS and SDV Samastipur )

       1.  Draw the graphs of 2x + y =  6 and 2x – y + 2 = 0 . Shade the region bounded by these lines and x-axis. Find the area of the shaded region.

      
         2.        Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines y – axis. Also determine this area.

 3.       A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Aarushi paid Rs 27 for a book kept for seven days. If fixed charges are Rs x and per day charge are Rs y. Write the linear equation representing the above information.

4.       A number is 27 more than number obtained by reversing its digits. If is unit’s and ten’s digit are x and y respectively, write the linear equation representing the above statement.

5.       Plot the points (3, 5) and (-1, 3) on a graph paper and verify that the straight line passing through these points also passes through the point (1, 4).

6.       A three – wheeler scooter charges Rs 15 for first kilometer and Rs 8 each for every subsequent kilometer. For a distance of x km, an amount of Rs y is paid. Write the linear equation representing the above information.

7.       The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten’s digit of the number are x and y respectively, then write the linear equation representing the above statement.

8.       If the point (2, -2) lies on the graph of the linear equation 5x + ky = 4, find the value of K.

9.       Draw the graph of y = |x| .

10.   Draw the graph of the equation 2x + y = 6. Shaded the region bounded by the graph and the coordinate axes.           Also, find the area of the shaded region.

11.   Ravish tells his daughter Aarushi, “Seven years ago, I was seven  times as old as you were then. Also, three years from now, I shall be three times as old as you will be”. If present ages of Aarushi and ravish are x and y years respectively, represent this situation algebraically as well as graphically

12.   Aarushi was driving a car with uniform speed of 60 km/h. Draw distance – time graph. From the graph, find the distance travelled by Aarushi in (a) 2and 1/2Hours   (b) 1/2 hours

13.   Solve the equation 2x + 1 = x – 3, and represent the solution (s) on (i) the number line  (ii) the Cartesian plane.

14.   Draw the graph of each of the following linear equations in Cartesian plane x + 5 = 0

15.   Draw a graph of the equation (i) y = -3  (ii) 2y + 3 = 9

Answer

1.8 sq. units     

2. 13.5 sq. units    

3. X + 4y = 27     

4. X – y + 3 = 0     

6. Y = 8x + 7     

7. X + y = 11    

8. K=3  

10. 9 sq. units   

12. (i) 150 km   (ii) 30 km     

9th Linear Equation in two Variable [Guess paper] 2013

9th Linear Equation in two Variable [Sample Guess paper] 2013

[1 Mark Questions]

1. Which of the following is not a linear equation?

(a) ax + by + c = 0                 (b) 0x + 0y + c = 0              

(c) 0x + by + c = 0                 (d) ax + 0y + c = 0

2. Age of ‘x’ exceeds age of ‘y’ by 7 yrs. This statement can be expressed as linear equation as  

(a) x + y + 7 = 0                  (b) x – y + 7 = 0      

(c) x – y – 7 = 0                  (d) x + y – 7 = 0

3. Linear equation in one variable is :

(a) 2x = y      (b) y2 = 3y + 5   (c) 4x – y = 5   (d) 3t + 5 = 9t – 7

4. The condition that the equation ax + by + c = 0 represent 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             

5. 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

6. The general form of a linear equation in two variables is :

(a) ax + by + c = 0, where a, b, c are real  umbers and a, b ≠ 0  

(b) ax + b = 0, where a, b are real numbers and a ≠0

(c) ax² + bx + c = 0, where a, b, c are real numbers and a, b ≠ 0    

(d) none of these

7. The equation of the line whose graph passes through the origin, is :  

CBSE MATHEMATICS (Class-9) ch-Linear Equation in Two Variables

1.     Find four different solutions of the equation x+2y=6.

2.     Find two solutions for each of the following equations:
(i) 4x + 3y = 12 
(ii) 2x + 5y = 0
(iii) 3y + 4=0

3.     Write four solutions for each of the following equations: 
(i) 2x + y = 7 
(ii) πx + y = 9 
(iii) x = 4y.

4.     Given the point (1, 2), find the equation of the line on which it lies. How many such equations are there?

5.     Draw the graph of the equation
(i) x + y = 7
(ii) 2y + 3 = 9
(iii) y - x = 2
(iv) 3x - 2y = 4
(v) x + y - 3 = 0

6.     Draw the graph of each of the following linear equations in two variables:
(i) x + y = 4
(ii) x - y = 2
(iii) y = 3x 
(iv) 3 = 2x + y
(v) x - 2 = 0
(vi) x + 5 = 0
(vii) 2x + 4 = 3x + 1.

7.     If the point (3, 4) lies on the graph of the equation 3y=ax+7, find the value of ‘a’.

8.     Solve the equations 2x + 1 = x - 3, and represent the solution(s) on
(i) the number line,
(ii) the Cartesian plane.

9.     Draw a graph of the line x - 2y = 3. From the graph, find the coordinates of the point when
(i) x = - 5 
(ii) y = 0.

10.   Draw the graph of y = x and y = - x in the same graph. Also, find the coordinates of the point where the two lines intersect.