Question

draw the graph of each of the following linear equations in two variables
1)2x+3y=6
2)4x-y=-8

Answer 1

Answer:

i) x + y = 4 ii) x – y = 2 (iii) y = 3x (iv) 3 = 2x + y

Sol: (i) x + y = 4 ⇒ y = 4 – x

If we have x = 0, then y = 4 – 0 = 4

x = 1, then y = 4 – 1 = 3

x = 2, then y = 4 – 2 = 2

∴ We get the following table:

Plot the ordered pairs (0, 4), (1, 3) and (2, 2) on the graph paper. Joining these points, we get a line AB as shown below.

Step-by-step explanation:

Thus, the line AB is the required graph of x + y = 4.

(ii) x – y = 2

⇒ y = x – 2

If we have x = 0,then y = 0 – 2 = –2

x = 1,then y = 1 – 2 = –1

x = 2, then y = 2 – 2 = 0

Plot the ordered pairs (0, –2), (1, –1) and (2, 0) on the graph paper. Joining these points, we get a straight line PQ as shown below:

Thus, the line PQ is required graph of x – y = 2.

(iii) y = 3x

If x = 0, then y = 3(0) ⇒ y = 0

x = 1, then y = 3(1) ⇒ y = 3

x = –1, then y = 3(–1) ⇒ y = –3

HOPE IT IS HELPFUL