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Pair of Linear Equations in Two Variables Test - 9

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Pair of Linear Equations in Two Variables Test - 9
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  • Question 1
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    A system of linear equations is said to be consistent, if it has

    Solution

    A system of linear equations is said to be consistent if it has at least one solution or can have many solutions. If a consistent system has an infinite number of solutions, it is dependent. When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

  • Question 2
    1 / -0

    A system of linear equations is said to be inconsistent, if it has

    Solution

    A system of linear equations is said to be inconsistent, if it has no solution means two lines are running parallel and not cutting each other at any point.

  • Question 3
    1 / -0

    The system of linear equations a1x + b1y1 + c1 = 0 and a2x + b2y + c2 = 0​​​​​​​​​​​​​​  has no solution if

    Solution

    The system of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 has no solution because both the equation satisfy the condition i.e  a1/a2 = b1/b2 ≠ c1/c2

  • Question 4
    1 / -0

    The system of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 ​​​​​​​​​​​​​​​​​​​​​has infinitely many solutions if

    Solution

    The system of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0​​​​​​​​​​​​​​ has infinitely many solutions because both the equation satisfy the condition i.e  a1/a2 = b1/b2 = c1/c2

  • Question 5
    1 / -0

    The pair of equations x = 2 and y = – 3 has

    Solution

    Here, a unique solution of each variable of a pair of linear equations is given, therefore, it has one solution to a system of linear equations.

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