On comparing the ratios  find out whether the following pair o

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 Multiple Choice QuestionsShort Answer Type

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11. On comparing the ratios straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 find out whether the following pair of linear equations are consistent, or inconsistent.

space space space space space space 3 over 2 straight x plus 5 over 3 straight y equals 7 semicolon space 9 straight x minus 10 straight y equals 14


space space space space space space 3 over 2 straight x plus 5 over 3 straight y equals 7 semicolon space 9 straight x minus 10 straight y equals 14

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Hence, the given lines are intersecting. So the given pair of linear equations has exactly one solution and therefore it is consistent.
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12. On comparing the ratios straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 find out whether the following pair of linear equations are consistent, or inconsistent.

5x-3y=11 ; -10x + 6y = -22

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13. On comparing the ratios straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2 find out whether the following pair of linear equations are consistent, or inconsistent.

4 over 3 straight x space plus space 2 straight y equals 8 space semicolon space 2 straight x space plus space 3 straight y equals space 12

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 Multiple Choice QuestionsLong Answer Type

14. Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

x + y = 5, 2x + 2y = 10
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15. Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

x – y = 8, 3x – 3y = 16
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16. Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

2x + y – 6 = 0,      4x – 2y – 4 = 0
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17. Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

2x – 2y – 2 = 0, 4x – 4y – 5 = 0
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18.

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

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 Multiple Choice QuestionsShort Answer Type

19.

Given the linear equations 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representing of the pair so formed is :

(i) intersecting lines

(ii) parallel lines

(iii) coincident lines.

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20.

Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

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