Question

solve the system by the method of your choice.
\

$$\begin{cases} y = 4x - 4 8x - 8 = 2y \\end{cases}$$

Explanation:

Step1: Substitute \( y = 4x - 4 \) into \( 8x - 8 = 2y \)

Substitute \( y \) in the second equation: \( 8x - 8 = 2(4x - 4) \)

Step2: Simplify the right - hand side

Expand the right - hand side: \( 8x - 8 = 8x - 8 \)

Step3: Analyze the equation

Subtract \( 8x \) from both sides: \( 8x-8x - 8=8x - 8x-8 \), which gives \( - 8=-8 \)

This is an identity, which means that the two equations represent the same line. So, the system has infinitely many solutions of the form \( (x,4x - 4) \) where \( x \) is any real number.

Answer:

The system has infinitely many solutions, and the solutions are all ordered pairs \( (x,4x - 4) \) where \( x \) is a real number.