Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 5 - Solving Systems of Linear Equations - 5.7 - Systems of Linear Inequalities - Monitoring Progress - Page 274: 2

Answer

$(1,4)$ is a solution of the system.

Work Step by Step

The given system of linear inequalities is. $\Rightarrow y\geq 3x+1$ ...... (1) $\Rightarrow y\gt x-1$ ...... (2) Substitute $1$ for $x$ and $4$ for $y$ in each inequality. Inequality (1) $\Rightarrow y\geq 3x+1$ $\Rightarrow 4\geq 3(1)+1$ $\Rightarrow 4\geq 3+1$ $\Rightarrow 4\geq 4$ True. Inequality (2) $\Rightarrow y\gt x-1$ $\Rightarrow 4\gt 1-1$ $\Rightarrow 4\gt 0$ True. $(1,4)$ satisfy each inequality. Hence, $(1,4)$ is a solution of the system.
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