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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.

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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.

straight x over 4 equals 1 minus y over 6

for intersection with x-axis, put y = 0

therefore space space space x over 4 equals 1 space space rightwards double arrow space x space space equals space 4

Hence the point of intersection with x-axis is (4, 0).
For intersection with y-axis, put x = 0

$therefore space space space space space 1 minus straight y over 6 equals 0 space rightwards double arrow space straight y over 6 equals 1 space space rightwards double arrow space space space space straight y space equals space 6$

Hence the point of intersection with y-axis is (0, 6).

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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.