For the lines (y=2) and (y=9), how many solutions will there be?
Answer and explanation
Correct answer: No solution
A pair of linear equations has a solution at every common point of their graphs. The equation y=2 is a horizontal line containing points whose y-coordinate is 2, while y=9 is another horizontal line at height 9. Because 2 and 9 are different, no point can lie on both lines: a common point would need to have y=2 and y=9 simultaneously. The lines are distinct and parallel, so the system has zero solutions. Hence option B is correct. Infinitely many solutions would occur if both equations represented the same line, one solution would require intersecting lines, and two solutions cannot occur for two distinct linear lines.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
A pair of linear equations has a solution at every common point of their graphs. The equation y=2 is a horizontal line containing points whose y-coordinate is 2, while y=9 is another horizontal line at height 9. Because 2 and 9 are different, no point can lie on both lines: a common point would need to have y=2 and y=9 simultaneously. The lines are distinct and parallel, so the system has zero solutions. Hence option B is correct. Infinitely many solutions would occur if both equations represented the same line, one solution would require intersecting lines, and two solutions cannot occur for two distinct linear lines.
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..
