Graphical Solutions of Pair of Linear Equations in Two Variables

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  • Q1

    The coordinates of the points where the lines 5x – y = 7 and 10x + y = 15 meet the y-axis are:

    Marks:1
    Answer:

    (0, –7), (0, 15)

    Explanation:

    Since any point on the Y-axis is in the form (0, k), i.e., x coordinate is equal to zero.

    So, 5x – y = 7 and 10x + y = 15
    5(0) –(k) = 7 and 10(0) + (k) = 15
    k = –7 and k = 15
    Required coordinates are (0, –7) and (0, 15).

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  • Q2

    The coordinates of the point where the line 2(x – 3) = y – 8 meet the x-axis is

    Marks:1
    Answer:

    (–1, 0)

    Explanation:

    Here y = 0

    2(x – 3) = 0 – 8

    (x – 3) = –4

    x = –1

    Required coordinate = (–1, 0)

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  • Q3

    The coordinates of the points where the lines 3x – y = 5 and 6x – y = 10 meet the y-axis are:

    Marks:1
    Answer:

    (0, –5), (0, –10)

    Explanation:

    Since any point on the Y-axis is in the form (0, k), i.e., x coordinate is equal to zero.

    So, 3x – y = 5 and 6x – y = 10

    3(0) – y = 5 and 6(0) – y = 10

    y = –5 and y = –10

    Hence, required coordinates are (0, –5), (0, –10).

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  • Q4

    If a system of linear equations has no solution, then the graphs of the equations

    Marks:1
    Answer:

    are parallel.

    Explanation:

    As parallel lines do not intersect each other. So, the equations have no common solution.

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  • Q5

    Which of the following system of equations is consistent?

    Marks:1
    Answer:

    4x + 6y – 7 = 0, 12x + 18y – 21 = 0

    Explanation:

    Consistency means the system of equations has at least one solution. Since B has infinitely many solutions, that system of equations is consistent.

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