121.

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.

x – 3y – 3 = 0
3x – 9y – 2 = 0

180 Views

122.

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.
2x + y = 5
3x + 2y = 8

197 Views

123.

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.
3x - 5y = 20
6x - 10y = 40

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124.
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.
x - 3y - 7 = 0
3x - 3y - 15 = 0

x - 3y - 7 = 0
3x - 3y - 15 = 0
The given pair of linear equations is
x - 3y - 7 = 0
3x - 3y - 15 = 0
Here, a₁ = 1, b₂ = -3, c₁ = -7
a₂ = 3, b₂ = -3, c₂ = -15
We see that

$straight a subscript 1 over straight a subscript 2 not equal to straight b subscript 1 over straight b subscript 2$

Hence, the given pair of linear equations has a unique solution.

To solve the given equations by cross multiplication method, we draw the diagram below :

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125.

For which values of a and b does the following pair of linear equations have an infinite number of solutions ?

2x + 3y = 7
(a - b) x + (a + b) y = 3a + b - 2

118 Views

126.

For which value of k will the following pair of linear equations have no solution?
3x + y = 1 (2k – 1) x + (k – 1) y = 2k + 1

505 Views

127.

Solve the following pair of linear equations by the substitution and cross-multiplication methods :
8x + 5y = 9
3x + 2y = 4

994 Views

128. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay ` 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ` 1180 as hostel charges. Find the fixed charges and the cost of food per day

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129. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :

A fraction becomes

1 half

when 1 is subtracted from the numerator and it becomes

1 fourth

when 8 is added to its denominator. Find the fraction.

134 Views

130. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

324 Views