Example Question - inconsistent systems
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Parallel Lines and Inconsistent Systems of Equations
It looks like the image shows a system of linear equations, and you might be asked to find the solution for this system. The equations in the image are: 1) \( y = -\frac{5}{4}x + 8 \) 2) \( y = -\frac{5}{4}x - 9 \) To solve these equations, we usually look for a point (x, y) that satisfies both equations. However, if you look closely at both equations, you'll notice that they both have the same slope, -5/4, which means they are parallel lines. Since parallel lines never intersect, they don't have a point in common. Therefore, this system of equations has no solution. In mathematical terms, this is known as an inconsistent system.
Parallel Lines and Inconsistent Systems of Equations
The equations provided in the image are: 1) \( y = -\frac{5}{4}x + 8 \) 2) \( y = -\frac{5}{4}x - 9 \) To solve these equations, you should first notice that both equations have the same slope, \(-\frac{5}{4}\), which indicates that the lines are parallel and therefore will never intersect each other. This means there is no single solution (x, y) that will satisfy both equations simultaneously. In other words, there is no solution to this system of equations; it is an inconsistent system.
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