Question

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how many solutions does the system of equations below have? -9y = -3x - 3 -12y = -4x - 4 no solution one solution infinitely many solutions

Explanation:

Step1: Rewrite equations in slope - intercept form ($y = mx + b$)

For $-9y=-3x - 3$, divide by $-9$: $y=\frac{1}{3}x+\frac{1}{3}$.
For $-12y=-4x - 4$, divide by $-12$: $y=\frac{1}{3}x+\frac{1}{3}$.

Step2: Analyze the relationship between the equations

Since both equations have the same slope ($m = \frac{1}{3}$) and the same y - intercept ($b=\frac{1}{3}$), they represent the same line.

Answer:

infinitely many solutions