What is the solution of (x+5y=22) and (x+2y=10) by elimination?
Answer and explanation
Correct answer: \((2,4)\)
Subtracting the second equation, \(x+2y=10\), from the first equation, \(x+5y=22\), gives \(3y=12\). Hence, \(y=4\). Substituting this into \(x+2y=10\) gives \(x+8=10\), so \(x=2\). Therefore, the solution is \((2,4)\). The close distractor \((4,3)\) does not satisfy either equation. Exam tip: Always substitute the ordered pair back into an original equation to verify the answer.
Frequently asked questions
What is the correct answer to this question?
\((2,4)\)
Why is this the correct answer?
Subtracting the second equation, \(x+2y=10\), from the first equation, \(x+5y=22\), gives \(3y=12\). Hence, \(y=4\). Substituting this into \(x+2y=10\) gives \(x+8=10\), so \(x=2\). Therefore, the solution is \((2,4)\). The close distractor \((4,3)\) does not satisfy either equation. Exam tip: Always substitute the ordered pair back into an original equation to verify the answer.
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..
