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TEXTBOOK QUESTIONS SOLVED

Exercise 4.1

1.  The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
(Take the cost of a notebook to be Rs. x and that of a pen to be Rs. y).

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Sol. Let cost of a notebook = Rs.x and cost of a pen = Rs. y.
According to given condition,
x = 2y ⇒  x  –  2y = 0.

2. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
(i) 2x + 3y = $9.3\overline 5$

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Sol. –   2x + 3y = $9.3\overline 5$ ⇒ 2x + 3y – $9.3\overline 5$ = 0
Here, a = 2,  b = 3,  c = – $9.3\overline 5$

(ii) $x - {y \over 5} - 10 = 0$

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Sol. –  $x - {y \over 5} - 10 = 0$
here a = 1,  $b = {{ - 1} \over 5}$ and   c = -10.

(iii) -2x + 3y = 6

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Sol. –            -2x + 3y = 6 ⇒   -2x  + 3y  – 6  = 0.
Here, a = -2, b = 3,  c = -6

(iv) x = 3y.

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Sol. –    x = 3y   ⇒ 1x – 3y  + 0 = 0
Here, a = 1, b = -3,  c  = -6

(v) 2x = – 5y

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Sol. –   2x = – 5y  ⇒   2x  + 5y   + 0 = 0
Here, a = 2, b = 5, c = 0

(vi) 3x + 2 = 0

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Sol. –    3x + 2 = 0   ⇒   3x   + 0y  + 2   = 0.
Here, a = 3,  b = 0,   c = 2.

(vii) y – 2 = 0

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Sol. –   y -2 = 0  ⇒ 0.x  + 1.y –  2  = 0
Here, a = 0,   b  = 1,   c = -2.

(viii) 5 = 2x.

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Sol. –    5 = 2x  ⇒  2x + 0.y – 5  = 0
Here, a = 2,  b = 0,  c = – 5.