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Linear Equations in Two Variables

Short Answer Type

31. 5. If x = –2, y = 6 is solution of equation 3ax + 2by = 6, then find the value of b from 2(a – 1) + 2(3b – 4) = 4.

If x = –2, y = 6 is solution of equation
3ax + 2by = 6, then

3a(-2) + 2b(6) = 6
$rightwards double arrow$ -6a + 12b = 6
$rightwards double arrow$ -a + 2b = 1 ...(1)
| dividing throughout by 6

Also

2(a - 1) + 2(3b - 4) = 4
$rightwards double arrow$ 2a - 2 + 6b -8 = 4
$rightwards double arrow$ 2a + 6b = 14
$rightwards double arrow$ a + 3b = 7 ....(2)
| Dividing throughout by 2
Adding (1) and (2), we get

5b = 8 $rightwards double arrow$ b = $8 over 5$
Putting b = $8 over 5$ in (1), we get

$negative straight a plus 2 open parentheses 8 over 5 close parentheses equals 1$
$rightwards double arrow space space space space space space space space space space straight a space equals space 16 over 5 minus 1 equals 11 over 5 Hence comma space space space space straight a space equals space 11 over 5 comma space space straight b space equals space 8 over 5$

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32. The coordinates of the points given in the following table represent some of the solutions of the equation

y equals 3 over 2 space space x space minus 1

Find the missing values. Also find the coordinates of the points where the line cuts x-axis and y-axis.

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33. Find the coordinates of the points where the line representing the equation

straight x over 4 equals 1 minus y over 6

cuts the x-axis and the y-axis.

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34. Determine the point on the graph of the equation 2x + 5y = 20 where x-coordinate is

5 over 2

times its ordinate.

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35.

Find four different solutions of the equation

x + 2y = 6.

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36.

Find two solutions for each of the following equations:

(i) 2x – 3y = 12 (ii) 2x – 5y = 0

(iii) 3y – 4 = 0.

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37.

Find the value of a so that the following equation may have x = 1, y = 1 as a solution:

3x + ay = 6

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38.

Write the equation $straight y square root of 3 equals 8 straight x plus square root of 5$ in the form of ax + by + c =0. Check whether (0, 1) and $left parenthesis square root of 3 comma space 9 right parenthesis$ are the solutions of the equation.

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39. Find three different solutions for the equation 3x – 4y = –12.

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40. Find three different solutions for the equation 6x – 8y + 32 = 0.

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