At which point do the lines x + y = 11 and 2x − 3y = −3 intersect on the graph?
Answer and explanation
Correct answer: (6, 5)
From the first equation, y = 11 − x. Substituting this into the second equation gives 2x − 3(11 − x) = −3, so 5x = 30 and x = 6. Therefore, y = 11 − 6 = 5. Hence, the lines intersect at (6, 5). Exam tip: The intersection point on the graph represents the common solution of both linear equations.
Frequently asked questions
What is the correct answer to this question?
(6, 5)
Why is this the correct answer?
From the first equation, y = 11 − x. Substituting this into the second equation gives 2x − 3(11 − x) = −3, so 5x = 30 and x = 6. Therefore, y = 11 − 6 = 5. Hence, the lines intersect at (6, 5). Exam tip: The intersection point on the graph represents the common solution of both linear 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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