EXERCISE 4.3
Draw the graph of each of the following linear equations in two variables:
(1) 7+y=4 (11) x-y=2
(iii) y = 3x (iv) 3 = 2x +y
Answers
Answer:
Exercise 4.3
Question 1: Draw the graph of each of the following linear equation in two variables:
(i) x + y = 4 (ii) x – y = 2 (iii) y = 3x (iv) 3 = 2x + y
Solution: (i) The given equation is
x + y = 4
y = 4 – x …………….equation (1)
Now , putting the value x = 0 in equation (1)
y = 4 – 0 = 4. So the solution is (0, 4)
Putting the value x = 1 in equation (1)
y = 4 – 1 = 3. So the solution is (1, 3)
Putting the value x = 2 in equation (1)
y = 4 – 2 = 2. So the solution is (2, 2)
So, the table of the different solutions of the equation is
linear equations 1
linear equations 2
Solution:(ii) The given equation is
x - y = 2
x = 2 + y…………….equation (1)
Now , putting the value y = 0 in equation (1)
x = 2 + 0 = 2. So the solution is (2, 0)
Putting the value y = 1 in equation (1)
x = 2 + 1 = 3. So the solution is (3, 1)
Putting the value y = 2 in equation (1)
x = 2 + 2 = 4. So the solution is (4, 2)
So, the table of the different solutions of the equation is
linear equations 3
Solution:(iii) The given equation is
y = 3x
y = 3x …………….equation (1)
Now , putting the value x = 0 in equation (1)
y = 3 x 0 = 0. So the solution is (0, 0)
Putting the value x = 1 in equation (1)
y = 3 x 1 = 3. So the solution is (1, 3)
Putting the value x = 2 in equation (1)
y = 3 x 2 = 6. So the solution is (2, 6)
So, the table of the different solutions of the equation is
linear equations 4
Solution:(iv) The given equation is
3 = 2 x + y
2 x + y = 3
y = 3 – 2x …………….equation (1)
Now, putting the value x = 0 in equation (1)
y = 3 – 2 x 0
y = 3 – 0 = 3. So the solution is (0, 3)
Putting the value x = 1 in equation (1)
y = 3 – 2 x 1
y = 3 – 2 = 1. So the solution is (1, 1)
Putting the value x = 2 in equation (1)
y = 3 – 2 x 2
y = 3 – 4 = -1. So the solution is (2, -1)
So, the table of the different solutions of the equation is
linear equations 5