If ax + 3y = 25 and 2x - 3y = 5 have solution x = 5, what is the value of a?
Answer and explanation
Correct answer: 4
Because (x, y) = (5, y) is a common solution, it must satisfy both equations. Substitute x = 5 into 2x - 3y = 5: 10 - 3y = 5, so 3y = 5 and y = 5/3. Now use the first equation: 5a + 3(5/3) = 25, which simplifies to 5a + 5 = 25. Thus 5a = 20 and a = 4. Therefore option B is correct. The other values would make the first equation equal to 20, 30, or 35 after substitution rather than the required 25, so they cannot describe the stated solution.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Because (x, y) = (5, y) is a common solution, it must satisfy both equations. Substitute x = 5 into 2x - 3y = 5: 10 - 3y = 5, so 3y = 5 and y = 5/3. Now use the first equation: 5a + 3(5/3) = 25, which simplifies to 5a + 5 = 25. Thus 5a = 20 and a = 4. Therefore option B is correct. The other values would make the first equation equal to 20, 30, or 35 after substitution rather than the required 25, so they cannot describe the stated solution.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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