To determine the correct statement about the system of equations, we need to analyze the line formed by the two points given for the second equation: $(-12, 20)$ and $(4, 12)$.

1. Calculate the slope (m) of the line connecting these points: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 20}{4 - (-12)} = \frac{-8}{16} = -\frac{1}{2}$

2. Use the point-slope form to write the equation of the line: $y - y_1 = m(x - x_1)$ Using point $(4, 12)$: $y - 12 = -\frac{1}{2}(x - 4)$ Simplifying: $y - 12 = -\frac{1}{2}x + 2 \implies y = -\frac{1}{2}x + 14$

3. Examine the first line (represented by the graph). We need to check its slope and y-intercept to see if the lines are parallel, coincident, or intersecting.

4. Analysis:

   • If the slopes are the same and the y-intercepts are different, the system has no solution (the lines are parallel).
   • If the slopes are different, there will be exactly one solution (the lines intersect).
   • If the slopes and y-intercepts are the same, there are infinite solutions (the lines are coincident).

Conclusion:

• Without the graph of the first equation, we cannot definitively determine the relationship between the two lines.
• However, if you check the slopes and the intercepts, you can conclude which statement is true.

From the options:

• A: (0, 14) could be a solution if it lies on both lines.
• B: Infinite solutions occur if both equations represent the same line.
• C: No solution if the lines are parallel.
• D: (10, 5) could also be a solution depending on the first line.

To decide: Check the first equation's slope and intercept against $-\frac{1}{2}x + 14$.

Do you have the equation for the first line, or can you provide more details about the graph?