Question

solve the system.
$-\frac{1}{3}x + 1 = y$
$y = -\frac{1}{3}x + 1$
solution:
the solution is (3,0).
the solution is (0, -1).
there is no solution.
there are infinitely many solutions.

Explanation:

Step1: Analyze the equations

The system of equations is \( y = -\frac{1}{3}x + 1 \) and \( y = -\frac{1}{3}x + 1 \). These are the same linear equation.

Step2: Determine the number of solutions

For a linear system, if two equations are identical (same slope and same y - intercept), then every point that satisfies one equation will satisfy the other. So, there are infinitely many solutions.

Answer:

There are infinitely many solutions.