Question

1. solve by graphing \\(\

$$\begin{cases} y = \\dfrac{2}{5}x - 2 \\\\ 8x - 20y = 40 \\end{cases}$$

\\)

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

Start with $8x - 20y = 40$. Isolate $y$:
$-20y = -8x + 40$
$y = \frac{-8}{-20}x + \frac{40}{-20}$
$y = \frac{2}{5}x - 2$

Step2: Compare the two equations

First equation: $y = \frac{2}{5}x - 2$
Second equation (simplified): $y = \frac{2}{5}x - 2$
The two equations are identical.

Step3: Interpret graph result

Identical linear equations represent the same line. Every point on the line is a solution.

Answer:

All points on the line $y = \frac{2}{5}x - 2$ are solutions; the system has infinitely many solutions.