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Pair of Linear Equations in Two Variables

10th Class - CBSE - Mathematics - 2372 Questions - 0 Concepts

Important Questions

Q1 Subjective Hard
Solve the following systems of equations by the method of cross-multiplication:
$$ \dfrac { { a }^{ 2 } }{ x } -\dfrac { { b }^{ 2 } }{ y } =0$$
$$ \dfrac { { a }^{ 2 }b }{ x } +\dfrac { { b }^{ 2 }a }{ y } =a+b,x,y\neq 0$$

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Q2 Subjective Hard
Solve the following systems of equations by the method of cross-multiplication:

$$ax+by=\dfrac { a+b }{ 2 } $$

$$3x+5y=4$$

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Q3 Subjective Hard
Solve the following systems of equations by the method of cross-multiplication:
$$6(ax+by)=3a+2b$$
$$6(bx-ay)=3a-2b$$

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Q4 Subjective Hard
Solve the following systems of equations by the method of cross-multiplication:

$$ \dfrac { x }{ a } +\dfrac { y }{ b } =a+b$$

$$ \dfrac { x }{ { a }^{ 2 } } +\dfrac { y }{ { b }^{ 2 } } =2$$

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Q5 Subjective Hard
Solve the following systems of equations by the method of cross-multiplication:
$$x\left( a-b+\dfrac { ab }{ a-b }  \right) =y\left( a-b-\dfrac { ab }{ a+b }  \right) $$
$$x+y=2{ a }^{ 2 }$$

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Q6 Subjective Hard
Solve the following systems of equations by the method of cross-multiplication:

$$bx+cy=a+b$$

$$ax\left( \dfrac { 1 }{ a-b } -\dfrac { 1 }{ a+b }  \right) +cy\left( \dfrac { 1 }{ b-a } -\dfrac { 1 }{ b+a }  \right) =\dfrac { 2a }{ a+b } $$

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Q7 Subjective Hard
Solve the following systems of equations by the method of cross-multiplication:

$$ \dfrac { 2 }{ x } +\dfrac { 3 }{ y } =13$$

$$ \dfrac { 5 }{ x } -\dfrac { 4 }{ y } =-2$$

where $$ x\neq 0$$ and $$ y\neq 0$$

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Q8 Subjective Hard
Solve the following systems of equations by the method of cross-multiplication:

$$ \dfrac { x }{ a } + \dfrac { y }{ b } =2$$

$$ax-by=c$$

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Q9 Single Correct Hard
The equation of the line passing through the point $$P(1, 2)$$ and cutting the lines $$x + y - 5 = 0$$ and $$2x - y = 7$$ at $$A$$ and $$B$$ respectively such that the harmonic mean of $$PA$$ and $$PB$$ is $$10$$, is
  • A. $$y + 2 = \tan \left (\cos^{-1} \dfrac {11}{\sqrt {146}} + \cos^{-1} \dfrac {14}{5\sqrt {146}}\right ) (x + 1)$$
  • B. $$y - 2 = \tan \left (\cos^{-1} \dfrac {11}{\sqrt {146}} + \cos^{-1} \dfrac {14}{5\sqrt {146}}\right ) (x - 1)$$
  • C. None of the above
  • D. $$y - 2 = \tan \left (\cos^{-1} \dfrac {11}{\sqrt {146}} - \cos^{-1} \dfrac {14}{5\sqrt {146}}\right ) (x - 1)$$

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Q10 Subjective Hard
Find all two-digit numbers such that the sum of the digits constituting the number is not less than $$7$$; the sum of the squares of the digits is not greater than $$30$$; the number consisting of the same digits written in the  reverse order is not larger than half the given number.

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Questions 122475
Subjects 10
Chapters 93
Enrolled Students 65
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