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Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
A fraction becomes `1/3` when 1 is subtracted from the numerator and it becomes `1/4` when 8 is added to its denominator. Find the fraction.
Concept: undefined >> undefined
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?
Concept: undefined >> undefined
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Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Concept: undefined >> undefined
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Concept: undefined >> undefined
Solve the following system of equations:
`x/3 + y/4 =11`
`(5x)/6 - y/3 = -7`
Concept: undefined >> undefined
Solve the following systems of equations:
4u + 3y = 8
`6u - 4y = -5`
Concept: undefined >> undefined
Solve the following systems of equations:
`x + y/2 = 4`
`x/3 + 2y = 5`
Concept: undefined >> undefined
Solve the following systems of equations:
`x + 2y = 3/2`
`2x + y = 3/2`
Concept: undefined >> undefined
Solve the following system of equations:
`sqrt(2)x - sqrt(3)y = 0`
`sqrt(3)x - sqrt(8)y = 0`
Concept: undefined >> undefined
Solve the following system of equations:
`3x - (y + 7)/11 + 2 = 10`
`2y + (x + 11)/7 = 10`
Concept: undefined >> undefined
Solve the following systems of equations:
`2x - 3/y = 9`
`3x + 7/y = 2, y != 0`
Concept: undefined >> undefined
Solve the following system of equations:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5
Concept: undefined >> undefined
Solve the following systems of equations:
`1/(7x) + 1/(6y) = 3`
`1/(2x) - 1/(3y) = 5`
Concept: undefined >> undefined
Solve the following systems of equations:
`1/(2x) + 1/(3y) = 2`
`1/(3x) + 1/(2y) = 13/6`
Concept: undefined >> undefined
Solve the following system of equations:
`4/x + 3y = 14`
`3/x - 4y = 23`
Concept: undefined >> undefined
Solve the following systems of equations:
`10/(x + y) + 2/(x - y) = 4`
`15/(x + y) - 5/(x - y) = -2`
Concept: undefined >> undefined
Solve the following system of equations:
`(7x - 2y)/(xy) = 5`
`(8x + 7y)/(xy) = 15`
Concept: undefined >> undefined
Solve each of the following systems of equations by the method of cross-multiplication :
x + 2y + 1 = 0
2x − 3y − 12 = 0
Concept: undefined >> undefined
Solve the following system of equations by the method of cross-multiplication:
3x + 2y + 25 = 0
2x + y + 10 = 0
Concept: undefined >> undefined
Solve each of the following systems of equations by the method of cross-multiplication :
2x + y = 35
3x + 4y = 65
Concept: undefined >> undefined
