Let's solve this by analyzing the properties of the lines described by both equations in the system.

Step 1: Determine the Equation of the Given Line

The line in the graph passes through two clearly identifiable points:

1. Point $(20, 0)$
2. Point $(0, 20)$

To find the equation of this line, we can determine the slope $m$ using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting $(x_1, y_1) = (20, 0)$ and $(x_2, y_2) = (0, 20)$: $m = \frac{20 - 0}{0 - 20} = \frac{20}{-20} = -1$

Now, using the point-slope form $y = mx + b$ and the point $(0, 20)$, where $b = 20$: $y = -x + 20$

So, the equation of the line already graphed is: $y = -x + 20$

Step 2: Determine the Equation of the Second Line

The second line in the system passes through the points $(-12, 20)$ and $(4, 12)$. We can find its slope $m$ similarly: $m = \frac{12 - 20}{4 - (-12)} = \frac{-8}{16} = -\frac{1}{2}$

Using the point-slope form $y = mx + b$ and the point $(4, 12)$, we can solve for $b$: $12 = -\frac{1}{2}(4) + b$ $12 = -2 + b$ $b = 14$

So, the equation of the second line is: $y = -\frac{1}{2}x + 14$

Step 3: Determine if There’s an Intersection (Solution to the System)

To find the solution to the system, set the two equations equal to each other and solve for $x$: $-x + 20 = -\frac{1}{2}x + 14$

Add $\frac{1}{2}x$ to both sides: $-\frac{1}{2}x + 20 = 14$

Subtract 20 from both sides: [ -\frac{1}{2