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Linear Equations in Two Variables

Short Answer Type

1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

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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:

2 x plus 3 y equals 9.3 space top enclose 5

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3. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

straight x minus straight y over 5 minus 1 equals 0

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4. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

- 2x + 3y = 6

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5. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

x = 3y

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6. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

2x = - 5y

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7. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

3x + 2 = 0

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8. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

y - 2 = 0

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9. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

5 = 2x

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10. Express the following statement as a linear equation in two variables by taking present ages (in years) of father and son as x and y, respectively. Age of father 5 years ago was two years more than 7 times the age of his son at that time.

Let the present ages of father and son be x years and y years respectively.

Then,

Age of father 5 years ago = (x – 5) years

Age of his son 5 years ago = (y – 5) years
According to the question,
x – 5 = 7(y – 5) + 2
⇒ x – 5 = 7y – 35 + 2
⇒ x – 7y + 28 = 0
which is the required linear equation in two variables.

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