If (4a+3b=276) and (2a+5b=250), what is the value of (a)?
Answer and explanation
Correct answer: \(a=45\)
Multiply the second equation, \(2a+5b=250\), by 2 to get \(4a+10b=500\). Subtracting \(4a+3b=276\) gives \(7b=224\), so \(b=32\). Substituting this into \(2a+5b=250\) gives \(2a+160=250\), hence \(a=45\). For example, \(a=40\) does not satisfy both equations together. Exam tip: in elimination, first make the coefficients of one variable equal.
Frequently asked questions
What is the correct answer to this question?
\(a=45\)
Why is this the correct answer?
Multiply the second equation, \(2a+5b=250\), by 2 to get \(4a+10b=500\). Subtracting \(4a+3b=276\) gives \(7b=224\), so \(b=32\). Substituting this into \(2a+5b=250\) gives \(2a+160=250\), hence \(a=45\). For example, \(a=40\) does not satisfy both equations together. Exam tip: in elimination, first make the coefficients of one variable equal.
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..
