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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

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

πx plus straight y equals 9

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

x = 4y

x = 4y

$rightwards double arrow$ $straight y space equals space straight x over 4$

Put x = 0, we get y = $0 over 4 space equals 0$

Put x = 4, we get y = $4 over 4 space equals 1$

Put x = 4, we get y = $fraction numerator negative 4 over denominator 4 end fraction equals space minus 1$

Put x = 2, we get y = $2 over 4 equals space 1 half$
$therefore$ Four solution are (0, 0) (4, 1), (-4, -1) and $open parentheses 2 comma 1 half close parentheses$