Explain what happens when a system of two linear equations is inconsistent. what effect does it have in obtaining a solution? what would the graph of such a system look like?

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graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.