Question

y = 5x - 1
-15x - 3y = 3
how many solutions does this linear system have?
one solution: (0, -1)
one solution: (1, 4)
no solution
infinite number of solutions

Explanation:

Step1: Substitute $y$ into second equation

Substitute $y=5x-1$ into $-15x-3y=3$:
$$-15x - 3(5x - 1) = 3$$

Step2: Expand and simplify left side

Distribute and combine like terms:
$$-15x -15x + 3 = 3$$
$$-30x + 3 = 3$$

Step3: Isolate $x$ term

Subtract 3 from both sides:
$$-30x = 0$$

Step4: Solve for $x$

Divide both sides by -30:
$$x = 0$$

Step5: Find corresponding $y$

Substitute $x=0$ into $y=5x-1$:
$$y = 5(0) - 1 = -1$$

Step6: Verify solution

Check if $(0,-1)$ satisfies $-15x-3y=3$:
$$-15(0) -3(-1) = 0 + 3 = 3$$
This matches the right-hand side.

Answer:

one solution: $(0, -1)$