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Linear Equations in Two Variables

Short Answer Type

11. Write the equation 2x = y in the form ax + by + c = 0 and find the values of a, b, c in the equation. How many solution this equation has?

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12. Compare the equation

straight x over 3 plus 3 over 2 y plus 4

= 2y – 3 and lx + my – n = 0 and write the value of l, m and n.

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13. Express the linear equation 7 = 2x in the form ax + by + c = 0 and also write the values of a, b and c

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

(i) 2x + 3y = 4.37
(ii) x - 4 =

square root of 3 space y

(iii) 4 = 5x - 3y
(iv) 2x = y

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15.

Write each of the following as an equation in two variables:

(i) x = – 5 (ii) y = 2

(iii) 2x = 3 (iv) 5y = 2.

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16.

Which one of the following options is true, and why?

y = 3x + 5 has

(i) a unique solution,
(ii) only two solutions,
(iii) infinitely many solutions.

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17. Write four solutions for each of the following equations:

2x + y = 7

2x +y = 7
2x + y = 7
⇒ y = 7 – 2x
Put x = 0, we get y = 7 – 2(0) = 7 – 0 = 7
Put x = 1, we gety = 7 – 2(1) = 7 – 2 = 5
Put x = 2, we get y = 7 — 2(2) = 7 – 4 = 3
Put x = 3, we get y = 7 – 2(3) = 7– 6 = 1
∴ Four solutions are (0, 7), (1, 5), (2, 3) and (3, 1).

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