Whether the point (4,0) is solution set of the system of equations x+y \leq 4

SchachtN 2021-10-12 Answered

Whether the point (4,0) is solution set of the system of equations x+y4,xy<4 or not, and also give reasons.

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Expert Answer

Arnold Odonnell
Answered 2021-10-13 Author has 109 answers

Consider the provide system are,
x+y4 and xy<4.
For check whether an ordered pair (4,0) is a solution of a system of linear inequalities x+y4 and xy<4, put the ordered pair (4,0) in the system of linear inequalities x+y4 and xy<4, Check whether the inequalities are satisfied or not.
Putting (4,0) in the first linear inequality x+y4 gives,
4+x4
44
Therefore, point (4,0) is satisfied for the linear inequality x+y4.
Putting (4,0) in the second linear equation xy<4 gives,
40<4
4<4
Therefore, point (4,0) does not satisfied for the linear equation xy<4.
Here the point (4,0) is true for first inequality, but false for second inequality, so it is not part of the solution set of provided inequalities.
Therefore, point (4,0) is not a solution of the provided system of inequalities.

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