Whether the point (4,0) is solution set of the system of equations x+y≤4,x−y&lt;4 or not, and also give reasons.

Question

Whether the point (4,0) is solution set of the system of equations x+y≤4,x−y&amp;lt;4 or not, and also give reasons.

Arnold Odonnell · Accepted Answer

Consider the provide system are, x+y≤4 and x−y&amp;lt;4. For check whether an ordered pair (4,0) is a solution of a system of linear inequalities x+y≤4 and x−y&amp;lt;4, put the ordered pair (4,0) in the system of linear inequalities x+y≤4 and x−y&amp;lt;4, Check whether the inequalities are satisfied or not. Putting (4,0) in the first linear inequality x+y≤4 gives, 4+x≤4 4≤4 Therefore, point (4,0) is satisfied for the linear inequality x+y≤4. Putting (4,0) in the second linear equation x−y&amp;lt;4 gives, 4−0&amp;lt;4 4&amp;lt;4 Therefore, point (4,0) does not satisfied for the linear equation x−y&amp;lt;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.

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

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