To solve the system of equations graphically, let’s first rewrite them for better understanding and visualization:
1. The first equation is [tex]\(y = -3x + 1\)[/tex].
2. The second equation given is [tex]\(-\frac{1}{3} y = x - \frac{1}{3}\)[/tex]. We can rewrite this into a more familiar form:
[tex]\[
-\frac{1}{3}y = x - \frac{1}{3}
\][/tex]
To get the equation in [tex]\(y = mx + b\)[/tex] form, multiply both sides by -3:
[tex]\[
y = -3x + 1
\][/tex]
Now we observe that both equations are identical:
[tex]\[
y = -3x + 1
\][/tex]
Since the equations are the same, they represent the same line. This means that every point on this line satisfies both equations.
Thus, the system of equations has infinitely many solutions, which are all points that lie on the line [tex]\(y = -3x + 1\)[/tex].
Therefore, the correct answer is:
[tex]\[ \text{solutions: all numbers on the line} \][/tex]
