A linear equation in two variables is an equation of the form ax plus by equals c where a, b, and c are constants. These equations describe straight l
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What is the difference between consistent and inconsistent systems?
A consistent system has at least one solution. If the equations have different slopes, they intersect at one point (unique solution). If they have the same slope and same line, they have infinitely many solutions. An inconsistent system has no solution, which happens when lines are parallel with different y-intercepts.
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How do you know if two lines are parallel?
Two lines are parallel if they have the same slope but different y-intercepts. In the form y equals mx plus b, parallel lines have the same m value but different b values. Parallel lines never intersect.
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Can you have a linear equation in three or more variables?
Yes, linear equations can have any number of variables. For example, 2x plus 3y minus z equals 10 is linear in three variables. In three dimensions, a linear equation represents a plane instead of a line. Systems can be solved similarly using elimination or substitution.
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