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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:
$\dfrac { { a }^{ 2 } }{ x } -\dfrac { { b }^{ 2 } }{ y } =0$
$\dfrac { { a }^{ 2 }b }{ x } +\dfrac { { b }^{ 2 }a }{ y } =a+b,x,y\neq 0$

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

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

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

$3x+5y=4$

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

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

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

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

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

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

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

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

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

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

$bx+cy=a+b$

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

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

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 $y\neq 0$

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

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

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

$ax-by=c$

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

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. $y - 2 = \tan \left (\cos^{-1} \dfrac {11}{\sqrt {146}} - \cos^{-1} \dfrac {14}{5\sqrt {146}}\right ) (x - 1)$

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

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.

Asked in: Mathematics - Pair of Linear Equations in Two Variables

1 Verified Answer | Published on 05th 09, 2020

Questions 122475
Subjects 10
Chapters 93
Enrolled Students 65