Solving 8x+3y=46 and 5x−3y=19 by elimination, what is the value of x?
Answer and explanation
Correct answer: 5
The elimination method removes one variable by adding or subtracting equations whose coefficients are opposites. Here the y-coefficients are +3 and −3, so add the equations directly: (8x + 3y) + (5x − 3y) = 46 + 19. The y terms cancel, leaving 13x = 65. Dividing both sides by 13 gives x = 5. Substituting x = 5 into the first equation gives 40 + 3y = 46, so y = 2; the second equation checks as 25 − 6 = 19. Hence option C is correct. Options A, B and D do not satisfy the resulting equation 13x = 65, so they cannot be the solution.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The elimination method removes one variable by adding or subtracting equations whose coefficients are opposites. Here the y-coefficients are +3 and −3, so add the equations directly: (8x + 3y) + (5x − 3y) = 46 + 19. The y terms cancel, leaving 13x = 65. Dividing both sides by 13 gives x = 5. Substituting x = 5 into the first equation gives 40 + 3y = 46, so y = 2; the second equation checks as 25 − 6 = 19. Hence option C is correct. Options A, B and D do not satisfy the resulting equation 13x = 65, so they cannot be the 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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