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Posted by on Tuesday, September 4, 2012 at 12:00pm.

How many solution sets do systems of linear inequalities have?
Do solutions to systems of linear inequalities need to satisfy both inequalities?
In what case might they not?

  • Algebra 1 - , Tuesday, September 4, 2012 at 12:47pm

    how many solution sets? from zero to the degree of the equation.

    do they have to satisfy both? Yes.

    In what case might they not? They have to satisfy both, or it is not a solution.

  • Algebra 1 - , Tuesday, September 4, 2012 at 12:53pm

    by definition, a solution set must satisfy all of the inequalities. Otherwise, it's not a solution.

    The number of solution sets depends on the particular problem. There may be none at all, as in

    x+y > 6
    x+y < 0

    Or there may be an unbounded one, as in

    x+y > 3
    x-y > 2

    or a bounded one, as in

    x+y > 3
    x-y > 2
    3x+y < 10

    a visit to wolframalpha.com will let you play around with some. For the last example, just type

    solve x+y > 3, x-y > 2, 3x+y < 10

    and it will show the solution sets and graph the region.

  • Algebra 1 - , Tuesday, June 4, 2013 at 5:16pm

    Do the equations x = 4y + 1 and x = 4y – 1 have the same solution?

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