Find the value of (x) from (4x+y=21) and (2x+y=11).
Answer and explanation
Correct answer: (x=5)
The two equations are \\(4x+y=21\\) and \\(2x+y=11\\). Both contain the same term \\(y\\) with the same coefficient. Subtracting the second equation from the first removes \\(y\\): \\(4x+y-(2x+y)=21-11\\). This gives \\(2x=10\\), and dividing both sides by 2 gives \\(x=5\\). Therefore, option D is correct.
A quick check confirms the result. Substituting \\(x=5\\) into the second equation gives \\(2(5)+y=11\\), so \\(y=1\\). The first equation then gives \\(4(5)+1=21\\), which is also true. The key method is elimination: equal terms with equal coefficients cancel when one equation is subtracted from the other.
Frequently asked questions
What is the correct answer to this question?
(x=5)
Why is this the correct answer?
The two equations are \\(4x+y=21\\) and \\(2x+y=11\\). Both contain the same term \\(y\\) with the same coefficient. Subtracting the second equation from the first removes \\(y\\): \\(4x+y-(2x+y)=21-11\\). This gives \\(2x=10\\), and dividing both sides by 2 gives \\(x=5\\). Therefore, option D is correct.
A quick check confirms the result. Substituting \\(x=5\\) into the second equation gives \\(2(5)+y=11\\), so \\(y=1\\). The first equation then gives \\(4(5)+1=21\\), which is also true. The key method is elimination: equal terms with equal coefficients cancel when one equation is subtracted from the other.
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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