If two lines have the same slope and the same intercept, how many solutions will their pair of equations have?
Answer and explanation
Correct answer: Infinitely many solutions
The slope-intercept form of a line is y = mx + c, where m is the slope and c is the y-intercept. If two lines have the same m and the same c, both equations describe exactly the same line, not two different lines. Every point lying on that common line satisfies both equations. Consequently, the pair has infinitely many common solutions. Option C is correct. Equal slopes with different intercepts would instead give parallel lines and no solution, while different slopes would produce one intersection and therefore a unique solution. The origin is not necessarily on the line.
Frequently asked questions
What is the correct answer to this question?
Infinitely many solutions
Why is this the correct answer?
The slope-intercept form of a line is y = mx + c, where m is the slope and c is the y-intercept. If two lines have the same m and the same c, both equations describe exactly the same line, not two different lines. Every point lying on that common line satisfies both equations. Consequently, the pair has infinitely many common solutions. Option C is correct. Equal slopes with different intercepts would instead give parallel lines and no solution, while different slopes would produce one intersection and therefore a unique solution. The origin is not necessarily on the line.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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