Olympiad – Class X – Mathematics - Pair of Linear Equations in Two Variables

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Question - 1

Which of the following is a linear equation?

  • A x-2y= 7
  • B x3-1 = 0
  • C x+\(\frac { 6 }{ x } \)=12
  • D \(\frac { x }{ 2 } +\frac { 3 }{ x } \)=14

Question - 2

Which of the following is a solution of 2p + 3q = 5?

  • A p = -1, q = 1
  • B p = 1, q = -1
  • C P = 1, q = 1
  • D p = -1, q = -1

Question - 3

Which of the following is the other name for a pair of linear equations in two variables?

  • A Consistent equations
  • B Simultaneous equations
  • C Inconsistent equations
  • D Dependent equations

Question - 4

What is the condition that a system of simultaneous equations a,x + b.y + C, = 0 and a2x + b2y + c2 = 0 must satisfy to have exactly one solution?

  • A \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } \)
  • B \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \neq \frac { { b }_{ 1 } }{ { b }_{ 2 } } \)
  • C \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { c }_{ 1 } }{ c_{ 2 } } \)
  • D \(\frac { b_{ 1 } }{ b_{ 2 } } =\frac { { c }_{ 1 } }{ c_{ 2 } } \)

Question - 5

How many solutions do the equations satisfying \(\frac { a_{ 1 } }{ a_{ 2 } } =\frac { { b }_{ 1 } }{ b_{ 2 } } =\frac { c_{ 1 } }{ c_{ 2 } } \)have

  • A One
  • B Two
  • C Three
  • D Infinitely many

Question - 6

What is a system of simultaneous equations called if it has no solution?

  • A Consistent system
  • B Independent system
  • C Inconsistent system
  • D Dependent system

Question - 7

How many solutions does the system of equations p+ 2q = 4 and 2p + 4q - 12 = 0 have?

  • A 0
  • B 1
  • C 2
  • D 3

Question - 8

What is a system of simultaneous equations called if its graph has intersecting lines?

  • A Inconsistent system
  • B Consistent system
  • C Dependent system
  • D Independent system

Question - 9

What is the nature of the graphs of a dependent system?

  • A Parallel lines
  • B Perpendicular lines
  • C Intersecting lines
  • D Coincident lines

Question - 10

What is the nature of the graphs of a system of linear equations with exactly one solution?

  • A Parallel lines
  • B Perpendicular lines
  • C Coincident lines
  • D Intersecting lines
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