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MATHS M.C.Q

Linear Equations in Two Variables · Rajasthan Board (RBSE) STD 9 (Rajasthan - English Medium). 189 questions.

Questions · Page 2 of 4

M.C.Q

Question 511 Mark
If (2, 0) is a solution of the linear equation 2x + 3y = k then the value of k is:
Answer
  1. 4
    Solution:
    Since, (2, 0) is a solution of the linear equation 2x + 3y = k, substituting x = 2 and y = 0 in the given equation,
    We have:
    2(2) + 3(0) = k
    ⇒ 4 + 0 = k
    ⇒ k = 4
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Question 531 Mark
The graph of every linear equation in two variables is a:
Answer
  1. Straight line.
    Solution:
    Because for one value of one variable their is only one and unique value of other variables.
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Question 541 Mark
The graph of the line y = 3 passes through the point:
Answer
  1. (2, 3)
    Solution:
    Since, the y coordinate is 3, the graph of the line y = 3 passes through the point (2, 3).
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Question 551 Mark
Cost of book (x) exceeds twice the cost of pen (y) by Rs 10. This statement can be expressed as linear equation.
Answer
  1. x - 2y - 10 = 0
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Question 571 Mark
How many linear equations can be satisfied by x = 2 and y = 3?
Answer
  1. Many.
    Solution:
    There are infinite many eqution which satisfy the given value x = 2, y = 3
    For example
    x + y = 5
    x - y = -1
    3x - 2y = 0
    Etc...
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Question 591 Mark
The graph of y = 6 is a line.
Answer
  1. 14
    Solution:
    For the equation 5x - 7y = 35, if y = 5,
    5x - 7y = 35
    y = 55
    x - 7.5 = 35
    5x - 35 = 35
    5x = 35 + 35
    5x = 70
    $\text{x}=\frac{70}{5}=14$
    x = 14.
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Question 601 Mark
The solution of equation x - 2y = 4 is:
Answer
  1. (4, 0)
    Solution:
    Explanation: Putting x = 4 and y = 0, on the L.H.S. of the given equation, we get;
    4 - 2 (0) = 4 - 0 = 4
    Which is equal to R.H.S.
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Question 611 Mark
The graph of y = 6 is a line.
Answer
  1. Parallel to x-axis at a distance 6 units from the origin.
    Solution:
    As y = a is an equation of a line parallel to x-axis at a distance of a unit from the origin.
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Question 621 Mark
Write the correct answer in the following:
The linear equation 2x – 5y = 7 has,
Answer
  1. Infinitely many solutions.
    Solution:
    2x – 5y = 7 is a linear equation in two variables. A linear equation in two variables has infinitely many solutions.
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Question 631 Mark
If (k, -3) lies on the line 3x - y = 6, then the value of ‘k’ is:
Answer
  1. 1
    Solution:
    (k, -3) lies on the line 3x - y = 6, it means that (k, -3) is a solutio of a line 3x - y = 6,
    So,
    3k -(-3) = 6
    3k + 3 = 6
    3k = 6 - 3
    3k = 3
    $\text{k}=\frac{3}{3}=1$
    k = 1.
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Question 641 Mark
Write the correct answer in the following:
The equation 2x + 5y = 7 has a unique solution, if x and y are,
Answer
  1. Natural numbers.
    Solution:
    The equation 2x + 5y = 7 has a unique solution if x, y are natural numbers.
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Question 651 Mark
The equation 3x + 4y = 7 has a unique solution, if x and y are:
Answer
  1. Natural numbers.
    Solution:
    3x + 4y = 7
    3x = 7 - 4y
    $\text{x} = 7−\frac{4\text{y}}{3}$
    The equation will have a unique solution only if x and y are natural numbers with only one value which is,
    For y = 1.
    $\text{x} = 7−\frac{4.1}{3}$
    $\text{x} = 7−\frac{4}{3}$
    $\text{x} = \frac{3}{3} = 1$
    x = 1
    I.e., x = 1, y = 1 will be unique value for this equation.
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Question 661 Mark
The graph of the line x = -2 passes through:
Answer
  1. (-2, 3)
    Solution:
    Because value of x co-ordinate is -2.
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Question 691 Mark
The positive solutions of the equation ax + by + c = 0 always lie in the:
Answer
  1. 1st quadrant.
    Solution:
    The positive solutions of the equation ax + by + c = 0 always lie in the 1st quadrant. Because in 1st quadrant both x and y have positive value.
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Question 701 Mark
The graph of the linear equation 2x - y = 4 cuts x-axis at:
Answer
  1. (2, 0)
    Solution:
    On x-axis, the y-co-ordinate is always 0.
    So, 2x - y = 4 will cut the x-axis where y = 0
    i.e. 2x = 4
    i.e. x = 2
    Thus, 2x - y = 4 will cut the x-axis at (2, 0).
    Hence, correct option is (a).
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Question 711 Mark
The equation x - 2 = 0 on number line is represented by:
Answer
  1. A point.
    Solution:
    The equation x - 2 = 0 is represented by a point on the number line.
    Therefore, the correct answer is (b).
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Question 721 Mark
Write the linear equation such that each point on its graph has an ordinates times its abscissa.
Answer
  1. y = 5x
    Solution:
    At x = 1
    y = 5.1 = 5
    y = 5
    (1, 5)
    At x = 2
    y = 5.2 = 10
    y = 10
    (2, 10)
    At x = 3
    y = 5.3 = 15
    y = 15
    (3, 15)
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Question 731 Mark
The graph of y = 4x will:
Answer
  1. Pass through the origin.
    Solution:
    The graph of y = 4x will pass through the origin (0, 0)
    y = 4x
    At x = 0
    y = 4.0
    y = 0
    So the graph y = 4x will pass from point (0, 0).
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Question 741 Mark
A linear equation in two variables is of the form ax + by + c = 0, where:
Answer
  1. a ≠ 0, b ≠ 0
    Solution:
    A linear equation in two variables is of the form ax + by + c = 0, where a ≠ 0, b ≠ 0.
    If the values of “a” and “b” are equal to 0, the equation becomes c = 0.
    Hence, the values of a and b should not be equal to 0.
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Question 751 Mark
The force applied on a body is directly proportional to the acceleration produced on it. The equation to represent the above statement is:
Answer
  1. y = kx
    Solution:
    Let force applied be y and acceleration produced be x. The force applied on a body is directly proportional to the acceleration produced on it.
    Yαx
    y = kx
    Where k is proportionality constant.
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Question 761 Mark
The linear equation 3x - y = x - 1 has:
Answer
  1. Infinitely many solutions.
    Solution:
    3x - y = x - 1
    y = 3x - x + 1
    y = 2x + 1
    This is linear equation of two variable. If we take any random value of x and solve y corresponding value of x. We will get infinite many solutions.
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Question 771 Mark
The cost of 2kg of apples and 1kg of grapes on a day was found to be ₹ 160. A linear equation in two variables to represent the above data is:
Answer
  1. 2x + y = 160
    Solution:
    Let the cost of apples be ₹ x per Kg and cost of grapes be ₹ y per Kg. The cost of 2kg of apples and 1kg of grapes on a day was found to be ₹ 160.
    So the equation will be 2x + y = 160.
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Question 781 Mark
Find the value of k, if x = 1, y = 2 is a solution of the equation 2x + 3y = k.
Answer
  1. 8
    Solution:
    2x + 3y = k
    k = 2 (1) + 3 (2)
    = 2 + 6 = 8
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Question 791 Mark
If the point (3, 4) lies on the graph of 3y = ax + 7 then the value of a is:
Answer
  1. $\frac{5}{3}$
    Solution:
    Given equation: 3y = ax + 7
    Also, (3, 4) lies on the graph of the equation.
    Putting x = 3, y = 4 in the equation, we get
    3 × 4 = 3a + 7
    ⇒ 12 = 3a + 7
    ⇒ 3a = 12 - 7 = 5
    $\Rightarrow\text{a}=\frac{5}{3}.$
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Question 801 Mark
Write the correct answer in the following:
If a linear equation has solutions (-2, 2), (0, 0) and (2, -2), then it is of the form,
Answer
  1. x + y = 0
    Solution:
    Thinking Process,
  1. Firstly, consider a linear equation ax + by + c = 0.
  2. Secondly, substitute all points one by one and get three different equations.
  3. Further, simplify the three equations and then substitute the values of a, b and c in the considered equation.
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Question 811 Mark
Any point on the x - axis is of the form.
Answer
  1. (x, 0)
    Solution:
    Any point on the x - axis is of the form (x, 0).
    On the x - axis, x can take any values, whereas y should be equal to 0.
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Question 821 Mark
The graph of x = - 4 is a straight line.
Answer
  1. Parallel to y-axis.
    Solution:
    We know that the general equation of a line parallel to y-axis is x = a.
    So x = -4 is a line parallel to y-axis.
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Question 831 Mark
The graph of the linear equation 2x + 3y = 6 cuts the y - axis at the point.
Answer
  1. (0, 2)
    Solution:
    Given that the graph of the linear equation 2x + 3y = 6 cuts the y - axis at the point.
    Let the point be “P”.
    Hence, the x - coordinate of point P is 0.
    Now, substitute x = 0 in the given equation,
    2 (0) + 3y = 6
    3y = 6
    y = 2
    Hence, the cooridnate point is (0, 2).
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Question 841 Mark
A linear equation in two variables is of the form ax + by + c = 0, where?
Answer
  1. a ≠ 0 and b ≠ 0
    Solution:
    A linear equation in two variables is of the form ax + by + c = 0 as a and b are coefficient of x and y so if a = 0 and b = 0 or either of one is zero in that case the equation will be one variable or their will be no equation respectively.
    Therefore when a ≠ 0 and b ≠ 0 then only the equation will be in two variable.
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Question 851 Mark
The value of k if x = 3 and y = -2 is a solution of the equation 2x - 13y = k is:
Answer
  1. 32
    Solution:
    We have to find the value of ‘k’ if x = 3 and y = -2 is a solution of the equation 2x - 13y = k
    2x - 13y = k
    2(3) - 13(-2) = k
    6 + 26 = k
    k = 32.
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Question 861 Mark
The graph of the linear equation y = x passes through the point.
Answer
  1. $(1,1)$
    Solution:
    y = x, ⇒ Both the coordinates are the same. Hence (1, 1) is correct option.
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Question 881 Mark
If we multiply or divide both sides of a linear equation with the same non - zero number, then the solution of the linear equation:
Answer
  1. Remains the same
    Solution:
    If we multiply or divide both sides of a linear equation with the same non - zero number, then the solution of the linear equation remains the same.
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Question 891 Mark
Write the correct answer in the following:
x = 5 and y = 2 is a solution of the linear equation,
Answer
  1. x + y = 7
    Solution:
    x = 5, y = 2 is a solution of the linear equation x + y = 7, as 5 + 2 = 7.
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Question 901 Mark
If x = 3 and y = -2 satisfies 2x - 3y = k, then the value of k is:
Answer
  1. 12
    Solution:
    If x = 3 and y = -2 satisfies 2x - 3y = k.
    It means x = 3 and y = -2 is a solution of equation 2x - 3y = k
    2 × 3 - 3(-2) = k
    6 + 6 = k
    k = 12
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Question 911 Mark
The equation of a line parallel to x-axis and 5 units below the origin is:
Answer
  1. y = -5
    Solution:
    The equation of a line parallel to x-axis and 5 units below the origin is y = -5 because when a line parallel to x axis in that case equation of line is y = a.
    Where a is the co-ordinate of y-axes and 5 units below the origin value x-coordinate is -5. So required equation is y = -5.
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Question 921 Mark
The linear equation 2x - 5y = 7 has:
Answer
  1. Infinitely many solutions
    Solution:
    The linear equation 2x - 5y has infinitely many solutions.
    Because, the equation 2x - 5y = 7 is a single equation, that involves two variables.
    Hence, for different values of x, we will get different values of y and vice - versa.
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Question 941 Mark
If (-2, 5) is a solution of 2x + my = 11, then the value of 'm' is:
Answer
  1. 3
    Solution:
    If (-2, 5) is a solution of 2x + my = 11
    then it will satisfy the given equation
    2(-2) + 5 m = 11
    -4 + 5m = 11
    5m = 11 + 4
    5m = 15
    $\text{m}=\frac{15}{5}=3$
    $\text{m}=3$
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Question 961 Mark
How many linear equations are satisfied by x = 2 and y = -3?
Answer
  1. Infinitely many.
    Solution:
    From Point (2, -3) there are infinitely many lines passing in every-direction.
    So (2, -3) is satisfied with infinite linear equations.
    Hence, correct option is (d).
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Question 971 Mark
The graph of a linear equation x - 5y + 3 = 0 cuts the x-axis at the point.
Answer
  1. (-3, 0)
    Solution:
    When a line cuts x-axis in that case y co-ordinate is 0.
    So to find the co-ordinate of x we put y = 0 in given equation,
    x - 5y + 3 = 0
    at y = 0
    x - 5.0 + 3 = 0
    x + 3 = 0
    x = -3
    So the co-ordinate are (-3, 0)
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Question 991 Mark
The graph of the linear equation 2x - 3y = 6, cuts the y-axis at the point:
Answer
  1. (0, -2)
    Solution:
    The linear equation 2x - 3y = 6, cuts the y-axis when x co-ordinate is 0.
    So we put x = 0 in given equation 2x - 3y = 6
    2 × 0 - 3y = 6
    0 - 3y = 6
    -y = 63
    -y = 2
    y = -2
    So the co-ordinates are (0, -2).
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Question 1001 Mark
The graph of the equation x + y = 4.
Answer
  1. Intersects both the axis.
    Solution:
    The graph of the equation x + y = 4,
    Put x = 0 cut y axis at y = 4,
    Put y = 0 cut x axis at x = 4.
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