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RD Chapter 7 Introduction to Euclid s Geometry Ex 7.1 Solutions

Question - 1 : - 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 = 12
(ii) x-┬а┬а-5 = 0
(iii) 2x + 3y = 9.35
(iv) 3x = -7y
(v) 2x + 3 = 0
(vi) y тАУ 5 = 0
(vii) 4 = 3x
(viii) y =┬а┬а

Answer - 1 : -

(i) -2x + 3y = 12
тЗТ┬а -2x + 3y тАУ 12 = 0
Here a -2, b = 3, c = тАУ 12
(ii) x тАУ┬а┬а┬а-5 = 0
Here a = 1, b =┬а┬а,c = -5
(iii) 2x + 3y = 9.35
тЗТ┬а 2x + 3y тАУ 9.35 = 0
Here a = 2, b = 3, c = тАУ 9.35
(iv) 3x = -7y
тЗТ┬а 3x + 7y + 0 = 0
Here a = 3, b = 7,c = 0
(v) 2x + 3 = 0
тЗТ 2x + 0y + 3 = 0
Here a = 2, b = 0, c = 3
(vi) y-5 = 0 тЗТ ox+y-5 = 0
Here a = 0, b = 1, c = -5
(vii) 4 = 3x
тЗТ 3x тАУ 4 = 0
тЗТ 3x + 0y тАУ 4 = 0
Here a = 3, b = 0, c = -4
(Viii) y=┬а┬а
┬атЗТ┬а┬а┬атАУ y+ 0 = 0
тЗТ┬а x-2y + 0 = 0
Here a = 1, y = -2, c = 0

Question - 2 : -
Write each of the following as an equation in two variables.
(i) 2x = -3
(ii) y = 3
(iii) 5x =┬а┬а
(iv) y =┬аx

Answer - 2 : -

(i) 2x = -3тЗТ┬а 2x + 3 = 0
тЗТ 2x + 0y + 3 = 0
(ii) y= 3 тЗТ┬а y-3=0
тЗТ┬а 0x+ y-3 = 0
(iii) 5x =┬а┬атЗТ 10x = 7
тЗТ┬а 10x + 0y тАУ 7 = 0
(iv) y=┬аxтЗТ2y = 3x
тЗТ 3x тАУ 2y + 0 = 0

Question - 3 : - The cost of ball pen is тВ╣5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.

Answer - 3 : -

Let cost of a fountain pen = тВ╣x
and cost of ball pen = тВ╣y
тИ┤ According to the condition,
y =-5
тЗТ┬а 2y = x тАУ 10
тЗТ┬а x тАУ 2y тАУ 10 = 0

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