Chapter 5, Systems of Equations and Inequalities - Section 5.5 - Systems of Inequalities - 5.5 Exercises - Page 474: 3

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If $(2,3)$ is a solution of a system of inequalities in $x$ and $y$, then plugging in $x=2,y=3$ into each inequality satisfies the expression. Plugging in $x=2,y=3$ into the first inequality, we get: $2(2)+4(3)=4+12=16\leq17$ Thus, this is satisfied. Plugging in $x=2,y=3$ into the second inequality, we get: $6(2)+5(3)=12+15=27\leq29$ Thus, this is also satisfied.