If 9x + 2y = 41 and 3x - 2y = -5, what is the value of x + 3y?
Answer and explanation
Correct answer: 24
The coefficients of y are +2 and -2, so add the equations to eliminate y: (9x + 2y) + (3x - 2y) = 41 + (-5), giving 12x = 36 and therefore x = 3. Substitute x = 3 into 3x - 2y = -5: 9 - 2y = -5, so -2y = -14 and y = 7. Now evaluate the requested expression separately: x + 3y = 3 + 3(7) = 3 + 21 = 24. Hence option D is correct. The original listed key and options did not include the computed value; 19, 20 and 21 are not equal to the required expression.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
The coefficients of y are +2 and -2, so add the equations to eliminate y: (9x + 2y) + (3x - 2y) = 41 + (-5), giving 12x = 36 and therefore x = 3. Substitute x = 3 into 3x - 2y = -5: 9 - 2y = -5, so -2y = -14 and y = 7. Now evaluate the requested expression separately: x + 3y = 3 + 3(7) = 3 + 21 = 24. Hence option D is correct. The original listed key and options did not include the computed value; 19, 20 and 21 are not equal to the required expression.
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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