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Draw the graph of (i) x – 7y = – 42 (ii) x – 3y = 6 (iii) x – y + 1 = 0 (iv) 3x + 2y = 12 - Mathematics

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Sum

Draw the graph of

(i) x – 7y = – 42

(ii) x – 3y = 6

(iii) x – y + 1 = 0

(iv) 3x + 2y = 12

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Solution

(i) x – 7y = – 42

x 0 7 14

`y=(x+42)/7 `

6 7 8
Points A B C

(ii) x – 3y = 6

x 6 12 18

`y =(x-6)/3 `

0 2 4
Points D E F

(iii) x – y + 1 = 0

      In tabular form

x 0 4
y = x+1 1 5
Points B

(iv) 3x + 2y = 12

x 0 2

`y =(12-13x)/2 `

6 3
Point C D

Note:*
(i) The graph of any linear equation is a line and every solution of equations lies on the graph of that equation.
(ii) If a point (a, b) is not on the line then this point is not a solution of given equation.

∵ (2, 9) and (4, 1) are on the line

∴ These two points are solution of given equation

But (1, 10) and (7, –4) are not on the line so these two are not solutions.

Concept: Pair of Linear Equations in Two Variables
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