Final answer:
The two given equations represent the same line because the second is just a multiple of the first. Therefore, the system of equations has infinitely many solutions.
Step-by-step explanation:
To determine how many solutions the system of equations has, we first need to examine their forms. The given equations are:
- 6x − 7y = 7
- 12x − 14y = − 7
By observing the coefficients, we can notice that the second equation is just a multiple of the first one (each term in the first equation has been multiplied by 2 to get the second equation). This suggests that both equations represent the same line. Therefore, we can confidently state that this system of equations has infinitely many solutions, as it represents two coincident lines.
To further clarify, a system of linear equations can have one solution (when the lines intersect at a single point), no solutions (when the lines are parallel and never intersect), or infinitely many solutions (when the lines are coincident). In this case, we are dealing with the latter scenario.