If the solution of ax + 2y = 17 and 3x - 2y = 7 has x = 4, what is the value of a?
Answer and explanation
Correct answer: 3
Because x = 4 is part of the solution, substitute it into the second equation first: 3(4) - 2y = 7, so 12 - 2y = 7. Thus -2y = -5 and y = 5/2. Now use both known values in the first equation: a(4) + 2(5/2) = 17. This simplifies to 4a + 5 = 17, so 4a = 12 and a = 3. Substitution back gives 3(4) + 2(5/2) = 12 + 5 = 17, confirming the result. Therefore option C is correct; the other values would make the first equation unequal to 17 for the stated solution.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Because x = 4 is part of the solution, substitute it into the second equation first: 3(4) - 2y = 7, so 12 - 2y = 7. Thus -2y = -5 and y = 5/2. Now use both known values in the first equation: a(4) + 2(5/2) = 17. This simplifies to 4a + 5 = 17, so 4a = 12 and a = 3. Substitution back gives 3(4) + 2(5/2) = 12 + 5 = 17, confirming the result. Therefore option C is correct; the other values would make the first equation unequal to 17 for 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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