Systems of Two-Variable Inequalities -- Chapter 3-3 Linear Systems Systems of Two-Variable Inequalities -- Chapter 3-3

Linear Inequalities Remember that inequalities graph like equations! Like y ≤ 3x +1 Graph as if it was y = 3x + 1 Except line is only solid if it is part of solution (meaning ≤ or ≥) otherwise DOTTED line (> or <) AND… must SHADE IN solution region (shading follows Y) Do this for EACH inequality in the system on the SAME PLANE (might want to hold shading till the end so it doesn’t get too messy!)

System of Inequalities

But what if the values are “discrete” Discrete values are ones without other values in between them, like whole numbers, or integers. Then we will not GRAPH the solution, because not all those in-between spaces actually exist! Make a TABLE! Use the (or an) inequality with most constraint in one variable (fewest possible solutions) and then list every possible solution for the other variable given each solution for the first. Circle the ones that ALSO work in the other inequality(s).

Table for System of Inequalities 𝑥+𝑦≥3 2𝑥+3𝑦≤12 𝑓𝑜𝑟 𝑤ℎ𝑜𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑜𝑛𝑙𝑦 2x + 3y ≤ 12 now select for x + y ≥3 Answers are: (0,3),(0,4),(1,2),(1,3),(2,1),(2,2),(3,0),(3,1),(3,2) (4,0),(4,1),(5,0),(6,0) x y 0, 1, 2, 3, 4 1 0, 1, 2, 3 2 0, 1, 2 3 4 0, 1 5 6 x y 0, 1, 2, 3, 4 1 0, 1, 2, 3 2 0, 1, 2 3 4 0, 1 5 6

Work Together Worksheet practice 3-3 p.153 #8 – 32 even