If the unique point of intersection of two lines is (r,s) and the lines are represented by (4r+s=29) and (r-s=1), what is the value of (r+s)?
Answer and explanation
Correct answer: 11
The intersection point (r,s) lies on both lines, so its coordinates satisfy both equations. From (r-s=1), we get (s=r-1). Substituting this into the first equation gives (4r+r-1=29), so (5r=30) and (r=6). Hence (s=5) and (r+s=6+5=11). Therefore, option C is correct. Exam tip: To find the intersection point, solve the two linear equations simultaneously.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
The intersection point (r,s) lies on both lines, so its coordinates satisfy both equations. From (r-s=1), we get (s=r-1). Substituting this into the first equation gives (4r+r-1=29), so (5r=30) and (r=6). Hence (s=5) and (r+s=6+5=11). Therefore, option C is correct. Exam tip: To find the intersection point, solve the two linear equations simultaneously.
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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