# Solution - Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method

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ConceptAlgebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method

#### Question

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

#### Solution

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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

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?

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Solve the following system of equations by the method of cross-multiplication. \frac{a}{x}-\frac{b}{y}=0;\text{}\frac{ab^{2}}{x}+\frac{a^{2}b}{y}=a^{2}+b^{2}; Where x ≠ 0, y ≠ 0

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#### Reference Material

Solution for concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method. For the courses 8th-10th CBSE, 9th - 10th SSC (English Medium)
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