Question

(b) \

$$\begin{cases} \\text{line 1: } \\ y = x \\\\ \\text{line 2: } \\ y = x + 4 \\end{cases}$$

describe the solution.

Explanation:

Step1: Identify slope of Line1

For $y=x$, slope $m_1=1$

Step2: Identify slope of Line2

For $y=x+4$, slope $m_2=1$

Step3: Compare slopes and intercepts

$m_1=m_2$, but y-intercepts $b_1=0
eq b_2=4$. Parallel lines never intersect, so no solution exists.

Answer:

There is no solution (the system is inconsistent).