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linear systems?
okay i'm doing linear systems and it says to decide whether the ordered pair is a solution of the linear system. (1,5) and the system is
3x - y = -2
-4x + 2y= 5
how would you do that?
and how do you state whether a linear system has one solution, many solutions, or no solution when there is a graph?
Let x=1 and y=5. Plug those into the equations. If the statements remain true after simplifying, then the ordered pair is a solution. If not, and you get something like "1=2" when you simplify, then you know the ordered pair isn't a solution.
When you're looking at lines like this on a two-dimensional graph, remember any point on a given line is a solution for that particular equation. So if there are points in common with the lines, then those points represent ordered pairs of solutions.
Two lines can either cross at some point (showing that there's one solution), completely overlap each other (showing infinately many solutions), or be parallel (showing no solutions).
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