Question

A system of linear equations contains two equations with the same slope. Select all of the correct statements.

A. The system represents perpendicular lines and has one solution. B. The system may represent two parallel lines and have no solution. C. The system may represent the same line and have infinitely many solutions. D. The system represents perpendicular lines and has two solutions.

Answer 1

B. The system may represent two parallel lines and have no solution.
C. The system my represent the same line and have infinitely many solutions.

Answer 2

B and C are correct statements.

Explanation:

Given is : A system of linear equations contains two equations with the same slope.

If the two given linear equations have the same slope but different y intercept, then the lines will be parallel. As we know that the parallel lines never meet or intersect, so such equations will have no solution.

Hence, B. The system may represent two parallel lines and have no solution. - is true.

Also if the given equations have same slope and same y intercept then it is the same line with infinite number of solutions.

Therefore, option C. The system may represent the same line and have infinitely many solutions. - is also true.