Linear Equations and Simultaneous (Linear) Equations

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  • Q1

    If the point (4, 3) is a solution of the equation 3x – ay = 6, find whether (–2, –6) is also a solution of the same equation.

    Marks:3
    Answer:

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  • Q2

    A boat goes 30 km upstream and 44 km downstream in 10hrs. In 13 hrs it goes 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.

    Marks:5
    Answer:

    Let the speed of boat in still water be x km/hr.
    The speed of stream = y km/h
    Speed of boat in upstream = (x – y) km/h
    Speed of boat in downstream = (x + y) km/h


    Hence, the speed of boat in still water is 8 km/hr and speed of stream is 3 km/hr.

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  • Q3

    The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

    Marks:5
    Answer:

    Let the tens and unit digits in the original number be x and y respectively. So, the number is 10x + y
    According to the given conditions,
    (10x + y) + (10y + x) = 66
    x + y = 6 … (1)
    Since the digits differ by 2, therefore
    x – y = 2 or y – x = 2
    If x – y = 2, then adding this equation and equation (1)
    we get, 2x = 8 or x = 4
    Substituting x = 4 in equation (1) we get,
    4 + y= 6
    y = 2
    Thus, we have x = 4, y = 2
    So, the number is 42.
    If y – x = 2, then adding this equation and equation (1) we get, 2y = 8 or y = 4.
    Substituting y = 4 in equation (1) we get,
    x + 4 = 6
    x = 2
    Thus, we have x = 2, y = 4
    So, the number is 24.
    Hence, there are two numbers, i.e., 42 and 24.

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  • Q4

    If the difference of two numbers is 26 and one number is three times the other, find the numbers.

    Marks:1
    Answer:

    Let x be greater number than y,then
    x - y = 26 ...(1)
    x = 3y ...(2)

    On solving the two equations, we get y = 13 and x = 39

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  • Q5

    Sum of two numbers in 48 and their difference is 20. Find the numbers.

    Marks:1
    Answer:

    Let x be greater number than y.
    x + y = 48 ...(1)
    x - y = 20 ...(2)

    On solving the two equations, we get x = 34 and y = 14

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