Question - Parallel Lines and Inconsistent Equations
Solution:
The equations provided are:1) $$ y = -\frac{5}{4}x + 8 $$2) $$ y = -\frac{5}{4}x - 9 $$To solve these equations, we need to find the values of $$x$$ and $$y$$ where both equations are satisfied, meaning where the lines intersect if these were graphed. However, when we observe the equations, we notice that the coefficients of $$x$$ in both equations are identical, and the constants are different. This means that the lines are parallel and never intersect.These equations represent parallel lines because they have the same slope, which is $$-\frac{5}{4}$$, but different y-intercepts. The y-intercept of the first equation is 8, and the y-intercept of the second equation is -9.Since the lines never meet, there is no solution to this system of equations—they are inconsistent. Therefore, there are no specific values of $$x$$ and $$y$$ that would solve both equations simultaneously.
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