Assignments
1. Solve the equation 2x + 1 = x – 2 & represent the solution on :
The number line Cartesian plane
Q. 2. The linear equation that converts the Fahrenheit to Celsius is as follows :-
F=(9/5)c + 32
Draw the graph of the linear equation .
If the temperature is 950F , what is the temperature in Celsius .
Is there a temperature which is numerically the same in both Fahrenheit and Celsius ? If yes, find it.
Q. 3. Express the following information in the form of linear equation :
In a one day International cricket match between India & Srilanka played in Nagpur, two Indian batsman together scored 176 runs .
The cost of a notebook is twice the cost of a pen.
Q. 4. Find two solutions for each of the following equations :
4x + 3y = 12
2x + 5y = 0
px + y = 3
Q. 5. Express each of the following linear equation in the standard form & hence find the values of a, b & c in each case :
x-[y/5]-10=0
2x = -5y
Q. 6. Check which of the following are solutions of the equation x – 2y = 4.
1. Solve the equation 2x + 1 = x – 2 & represent the solution on :
The number line Cartesian plane
Q. 2. The linear equation that converts the Fahrenheit to Celsius is as follows :-
F=(9/5)c + 32
Draw the graph of the linear equation .
If the temperature is 950F , what is the temperature in Celsius .
Is there a temperature which is numerically the same in both Fahrenheit and Celsius ? If yes, find it.
Q. 3. Express the following information in the form of linear equation :
In a one day International cricket match between India & Srilanka played in Nagpur, two Indian batsman together scored 176 runs .
The cost of a notebook is twice the cost of a pen.
Q. 4. Find two solutions for each of the following equations :
4x + 3y = 12
2x + 5y = 0
px + y = 3
Q. 5. Express each of the following linear equation in the standard form & hence find the values of a, b & c in each case :
x-[y/5]-10=0
2x = -5y
Q. 6. Check which of the following are solutions of the equation x – 2y = 4.
- √2 ,4√2
- (1,1)
- (4,0)
Q. 7. (a). How many solutions does the following linear equation & why ?
3x – y + 5 = 0
(b)Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
Q. 8. (a). Given the point (1,2), find the equation of a line on which it lies. How many such equations are there ?
(b)Give an equation of two lines passing through (2,14). How many more Such lines are there & why ?
Q. 9. Draw the graph of each of the following linear equation in two variables :
3 = 2x + y
y = 3x
Q. 10. The taxi fare in the city is as follows : For the first kilometer, the are is Rs. 8 & for the subsequent distance it is Rs. 5 per km. Write a linear equation for this information & draw its graph .
Q.11. Write the quadrant in which each of the following points lie :
(i) (–3, –5) (ii) (2, –5) (iii) (–3, 5) Also, verify by locating them on
the Cartesian plane.
Q. 12 Solve the equation 3x + 2 = 2x – 2 and represent the solution on the Cartesian plane
Q. 13. The taxi fair in a city is as follows:
For the first kilometer, the fare is Rs 10 and for the subsequent distance it is Rs 6 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information and draw its graph. From the graph, find the fare for travelling a distance of 4 km
Q.14. Is (1, 8) the only solution of y = 3x + 5? Give reasons.
Q.15. Write the coordinates of a point on x-axis at a distance of 4 units from origin in the positive direction of x-axis and then justify your answer.
3x – y + 5 = 0
(b)Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
Q. 8. (a). Given the point (1,2), find the equation of a line on which it lies. How many such equations are there ?
(b)Give an equation of two lines passing through (2,14). How many more Such lines are there & why ?
Q. 9. Draw the graph of each of the following linear equation in two variables :
3 = 2x + y
y = 3x
Q. 10. The taxi fare in the city is as follows : For the first kilometer, the are is Rs. 8 & for the subsequent distance it is Rs. 5 per km. Write a linear equation for this information & draw its graph .
Q.11. Write the quadrant in which each of the following points lie :
(i) (–3, –5) (ii) (2, –5) (iii) (–3, 5) Also, verify by locating them on
the Cartesian plane.
Q. 12 Solve the equation 3x + 2 = 2x – 2 and represent the solution on the Cartesian plane
Q. 13. The taxi fair in a city is as follows:
For the first kilometer, the fare is Rs 10 and for the subsequent distance it is Rs 6 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information and draw its graph. From the graph, find the fare for travelling a distance of 4 km
Q.14. Is (1, 8) the only solution of y = 3x + 5? Give reasons.
Q.15. Write the coordinates of a point on x-axis at a distance of 4 units from origin in the positive direction of x-axis and then justify your answer.
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