What is the solution of (6x+5y=2) and (4x-5y=18)?
Answer and explanation
Correct answer: \((2,-2)\)
Adding the two equations gives \((6x+5y)+(4x-5y)=2+18\), so \(10x=20\). Hence, \(x=2\). Substituting this into \(6x+5y=2\) gives \(12+5y=2\), so \(5y=-10\) and \(y=-2\). Therefore, the solution is \((2,-2)\). A close distractor such as \((3,-3)\) does not satisfy the first equation. Exam tip: when terms have opposite coefficients, adding the equations is a quick elimination method.
Frequently asked questions
What is the correct answer to this question?
\((2,-2)\)
Why is this the correct answer?
Adding the two equations gives \((6x+5y)+(4x-5y)=2+18\), so \(10x=20\). Hence, \(x=2\). Substituting this into \(6x+5y=2\) gives \(12+5y=2\), so \(5y=-10\) and \(y=-2\). Therefore, the solution is \((2,-2)\). A close distractor such as \((3,-3)\) does not satisfy the first equation. Exam tip: when terms have opposite coefficients, adding the equations is a quick elimination method.
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..
