For the two variables x and y, the equations \(2x+2y=72\) and \(3x-3y=18\) are given. What is the point of intersection of the graphs of these two linear equations?
Answer and explanation
Correct answer: \((21,15)\)
Simplifying the equations gives \(x+y=36\) and \(x-y=6\). Adding them yields \(2x=42\), so \(x=21\). Substituting this into \(x+y=36\) gives \(y=15\). Therefore, the graphs intersect at \((21,15)\). Option B incorrectly reverses the values of x and y, so it is not the solution. Exam tip: In the graphical method, the point of intersection represents the common solution of both equations.
Frequently asked questions
What is the correct answer to this question?
\((21,15)\)
Why is this the correct answer?
Simplifying the equations gives \(x+y=36\) and \(x-y=6\). Adding them yields \(2x=42\), so \(x=21\). Substituting this into \(x+y=36\) gives \(y=15\). Therefore, the graphs intersect at \((21,15)\). Option B incorrectly reverses the values of x and y, so it is not the solution. Exam tip: In the graphical method, the point of intersection represents the common solution of both equations.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
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