Find the value of (x) from (4x+y=14) and (x+y=5).
Answer and explanation
Correct answer: (x=3)
The two equations describe relationships between the same two unknown numbers, x and y. Because the coefficient of y is 1 in both equations, subtracting one equation from the other removes y completely. This leaves an equation containing only x, which can be solved directly. This is the elimination method, because one variable is eliminated by combining the equations.
Subtract the second equation from the first: \(4x+y-(x+y)=14-5\). The y terms cancel, so \(3x=9\). Dividing both sides by 3 gives \(x=3\). Substitution can check it: if x is 3, then \(3+y=5\), so y is 2, and \(4(3)+2=14\). Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
(x=3)
Why is this the correct answer?
The two equations describe relationships between the same two unknown numbers, x and y. Because the coefficient of y is 1 in both equations, subtracting one equation from the other removes y completely. This leaves an equation containing only x, which can be solved directly. This is the elimination method, because one variable is eliminated by combining the equations.
Subtract the second equation from the first: \(4x+y-(x+y)=14-5\). The y terms cancel, so \(3x=9\). Dividing both sides by 3 gives \(x=3\). Substitution can check it: if x is 3, then \(3+y=5\), so y is 2, and \(4(3)+2=14\). Therefore option B is correct.
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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