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Linear Equations in Two Variables

Short Answer Type

41. If the point (2, –4) lies on the graph of the equation 2y = ax – 10, then find the value of a. Now express this as a linear equation in two variables.

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42. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k. Express y in terms of x and find the value of y when x = –1.

Solution not provided.

Ans. k = 7; $straight y equals fraction numerator 7 minus 2 straight x over denominator 3 end fraction semicolon space 3$

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43. Write six solutions for the equation 2x + y = 7.

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44. Express y in terms of x, it being given that 3x + y – 9 = 0. Check whether the points (3, 0) and (2, 2) lie on the equation.

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45. If x = 2 and y = – 1 is a solution of the equation ax – y = 5, find the value of a, also two more solutions of the equation.

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46. (2, –3) is a solution of the equation 2(x + 1) – 7(y – 2) = k, find the value of k. Find two more solutions also.

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47. Write the following equation in the form ax + by + c = 0 and find values of a, b and c : 4 = 3x – 5y. Check whether (1, –1) and (3, 1) are solutions of this equation or not.

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48. If the point (–2,4) lies on the graph of the equation (a – 1) y + 3x = 6, find four other solutions of this equation.

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49. There are few families residing in a locality. For a festival some families donated र 100 each and the other families donated र 50 each. The total money collected was र 44,450. Express this in the form of an equation in two variables. Using this equation, find the number of families who donated र 100 each if the number of families donating र 50 is 111.

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50. Check whether (3, 1), (1, 3) and (0, 8) are the solutions of the equation 3x – y = 8.

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