Certainly! Let's solve the system of equations step by step.
We are given the following system of equations:
1. [tex]\( x = 2y - 5 \)[/tex]
2. [tex]\( -3x = -6y + 15 \)[/tex]
First, let's simplify the second equation:
[tex]\[ -3x = -6y + 15 \][/tex]
We can divide every term by -3 to make it simpler to work with:
[tex]\[ x = 2y - 5 \][/tex]
Now we observe that both equations simplify to:
[tex]\[ x = 2y - 5 \][/tex]
In this situation, we recognize that the above two equations are essentially identical. Since both equations represent the same line, every point [tex]\((x, y)\)[/tex] that satisfies one equation also satisfies the other.
This situation leads us to the following conclusions:
- Both equations are dependent on each other, meaning they describe the same line.
- Therefore, there are infinitely many solutions available, consisting of all points that lie on the line [tex]\( x = 2y - 5 \)[/tex].
Thus, the correct answer to the system of equations is:
d. Infinite solutions.
