LINEAR EQUATIONS IN TWO VARIABLES
1. Find two solutions of the linear equation 5x – 4y = - 8
2. Draw the graph of the linear equation 2x + 3y = 12. At what points the graph of the
equation cuts the x-axis and the y axis
3. Draw the graphs of the equations x + y = 6 and 2x + 3y = 16 on the same graph paper.
Find the coordinates of the points where the two lines intersect
4. Draw the graph of the following equation 2( x + 1) = 3 ( y - 1) - 4 and check whether
the point (3,-1) lies on the line
5. Draw the graph of y=- 5 and y = 5 on the same graph. Are the lines parallel? Find the
point of intersection of two lines
6. The taxi fare in a city is such that Rs 50 is fixed amount and Rs 16 per km is charged.
Taking the distance covered as x km and total fare as Rs y, write a linear equation in x
and y
7. If present age of son and father are expressed by x and y respectively and after ten
years father will be twice as old as his son. Write the relation between x and y
8. If the cost of 5 tables exceeds the cost of eight chairs by Rs. 150. Write the linear
equation in two variables to represent the statement. Also find the cost of 1 table if
the cost of one chair is RS. 240
9. Give the geometric representation of 2x + 1 = x - 4 as an equation in (a)one variable
(b) two variable
10. Give the equation of two lines passing throw (2, 14). How many more such lines are
there and why
11. If (2,5) is a solution of the equation 2x + 3y = m, find the value of m (m = 19)
12. For what value of k does the point (k, -3) lies on the line 3x - y = 6
(k = 1)
13. Write 13x -12y = 25 as y=mx + c. Hence find m and c. Verify if x = 1, y = 1 is a solution
(m= 13/12, c = - 25/12)
14. If (2, 3) and (4,0) lie on the graph of the equation ax + by = 1. Find the value of a and
b. Plot the graph of the equation obtained
(a =1/4, b = 1/6)
15. Express y in terms of x, given that x/5 + 2y = 3. Check whether (-5, 2) is a solution of
the given equation
16. Write each of the following as an equation in two variables (in standard form):
(a) x = -5 (b) y = 2 (c) 2x = 3 (d) 5y = 2
17. Frame a linear equation in the form ax + by + c = 0 by using the given values of a, b and
c: a = -2, b = 3, c = 4
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Answers
Given : linear equation 5x – 4y = - 8
2x + 3y = 12
To Find : two solutions of the linear equation 5x – 4y = - 8
Draw the graph of the linear equation 2x + 3y = 12.
Solution:
5x – 4y = - 8
x = 0
=> -4y = -8
=> y = 2
( 0 ,2 ) is one solution
Put y = 0
=> x = -1.6
(-1.6 , 0) is another solution
2x + 3y = 12
cut x axis => y = 0
=> x = 6
( 6 ,0)
cut y axis => x = 0
=> y = 4
=> ( 0 , 4)
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Answer:
5x – 4y = - 8
x = 0
=> -4y = -8
=> y = 2
( 0 ,2 ) is one solution
Put y = 0
=> x = -1.6
(-1.6 , 0) is another solution
2x + 3y = 12
cut x axis => y = 0
=> x = 6
( 6 ,0)
cut y axis => x = 0
=> y = 4
=> ( 0 , 4)
Step-by-step explanation: