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When determining if a given point satisfies an equation, we substitute the point into the equation and simplify. If the resulting statement is true, then the point is contained in the solution set of the equation.
For systems of inequalities, we can use the same method. However, substituting the point must create true statements in *every* inequality in the system. Let's test to see if $(3,11)$ is a solution to the given system.
Since $11$ is greater than $7$ and less than $17,$ both statements are true. Therefore, the point $(3,11)$ is contained in the solution set of the system.

${y>x+5y<3x+8 (I)(II) $

$⎩⎪⎨⎪⎧ 11>? (3)+511<? 3(3)+8 $

Multiply$(II):$ Multiply

$⎩⎪⎨⎪⎧ 11>? 3+411<? 9+8 $

AddTermsAdd terms

${11>711<17 $