Final answer:
The system of equations 5x - 6y = 0 and y = x has infinitely many solutions because every point on the line y = x satisfies the first equation. Thus, the correct answer is D) Infinitely many solutions.
Step-by-step explanation:
To solve the given system of equations by substitution, you have 5x - 6y = 0 and y = x. First, substitute the second equation into the first:
This simplifies to:
Since y = x, it then follows that:
Thus, the solution to the system of equations is the point (0,0), which corresponds to option A.
It is important to check whether this solution is the only solution or if there are infinitely many solutions. If we substitute y = x back into the original equation 5x - 6y = 0:
- 5(y) - 6(y) = 0
- -y = 0
- y = 0
we find it produces a true statement for all values of y that are equal to x, indicating that every point on the line y = x is a solution. Therefore, the correct answer is D) Infinitely many solutions.