To solve this system of equations by graphing, we'll first convert each equation into slope-intercept form ($y = mx + b$) and then plot them.

The given system of equations is:

$2x - 5y = 20 \quad \text{(Equation 1)}$ $4x - 10y = -40 \quad \text{(Equation 2)}$

Step 1: Convert each equation to slope-intercept form

Equation 1: $2x - 5y = 20$

• Solve for $y$: $2x - 5y = 20 \quad \Rightarrow \quad -5y = -2x + 20$ $y = \frac{2}{5}x - 4$

Equation 2: $4x - 10y = -40$

• Solve for $y$: $4x - 10y = -40 \quad \Rightarrow \quad -10y = -4x - 40$ $y = \frac{2}{5}x - 4$

Step 2: Graph the equations

Both equations simplify to the same line: $y = \frac{2}{5}x - 4$.

Step 3: Analyze the system

Since both equations represent the same line, they overlap completely. This means that every point on the line is a solution to the system