Question - Parallel Lines: Inconsistent System of Equations
Solution:
The image shows two equations, which form a system of linear equations:1) $$ y = -\frac{5}{4}x + 8 $$2) $$ y = -\frac{5}{4}x - 9 $$To solve this system, we would normally look for values of $$ x $$ and $$ y $$ that satisfy both equations. However, if we compare the two equations, we can see that they both have the same slope, -5/4, but different y-intercepts.Since they both have the same slope, this means that the lines are parallel to each other. Parallel lines never intersect, which means that there is no solution to the system (they do not share any common points). In the context of systems of equations, this situation is known as an "inconsistent system."
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