Question

1. solve the system of equations.

3y - 9x = -6
4y - 12x = -8

Explanation:

Step1: Simplify first equation

Divide by 3:
$$\frac{3y - 9x}{3} = \frac{-6}{3}$$
$$y - 3x = -2$$
$$y = 3x - 2$$

Step2: Simplify second equation

Divide by 4:
$$\frac{4y - 12x}{4} = \frac{-8}{4}$$
$$y - 3x = -2$$
$$y = 3x - 2$$

Step3: Analyze the two equations

Both equations simplify to the same linear equation, meaning they represent the same line. All points on this line are solutions.

Answer:

All ordered pairs $(x, 3x-2)$ where $x$ is any real number (infinitely many solutions, as the two equations are dependent and represent the same line).