Answer:
C
Step-by-step explanation:
Whenever our simplification of a linear equation ends in a true statement, in this case 6=6, then our linear equation has infinitely many solutions.
Therefore, our answer is C.
In general:
- If we get a true statement (e.g. x=x, 6=6, etc.), then our linear equation has infinitely many solutions.
- If we get a false statement (e.g. 0=1, 7=2, etc.), then our linear equation has no solution.
- And if we get a variable equal to a value (x=2, x=7/2, etc.), then our linear equation has exactly one solution.
This is because if we get a true statement, then this implies that the two linear equations are the exact same line.
If we get a false statement, this implies that the two lines are parallel but not the same. They will never intersect.
And if we get a variable equal to a value, this implies that the two lines are not the same but they will intersect. Since they are lines, they will only intersect once, giving us only one solution.