Question

determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
$3x + 2y = 8$
$-6x - 4y = -16$

Explanation:

Step1: Analyze the second equation

Notice that the second equation can be simplified by dividing every term by -2.
$$\frac{-6x}{-2} + \frac{-4y}{-2} = \frac{-16}{-2}$$

Step2: Simplify the second equation

After dividing, the second equation becomes identical to the first.
$$3x + 2y = 8$$

Step3: Interpret the result

Since both equations represent the same line, every point on the line is a solution.

Answer:

The system has infinitely many solutions.