Question

systems of linear inequalities
graphing linear inequality systems (a.rei.12)
system of linear inequalities

y = -3x + 6
y = x + 2
one solution:
(1,3)

y > -3x + 6
0 > -3(0) + 6
0 > 0 + 6
0 > 6
false

y ≤ x + 2
0 ≤ 0 + 2
0 ≤ 2

y = 2x + 6
y = 2x - 1
no solution

y = -x + 4
2y = -2x + 8
infinite
solutions

multiple-choice question
what does 0 ≤ 2 imply?
since 0 ≤ 2 is true, we must shade on the same side of the line.
since 0 ≤ 2 is false, we must shade on the same side of the line.
since 0 ≤ 2 is true, we must shade on the opposite side of the line.
since 0 ≤ 2 is false, we must shade on the opposite side of the line.

Explanation:

To determine the implication of \(0 \leq 2\) in the context of graphing linear inequalities, we first check the truth value of \(0 \leq 2\). Since \(0\) is less than or equal to \(2\), this statement is true. When testing a point (like \((0,0)\) here) in a linear inequality, if the test is true, we shade the side of the line that contains the test point (the same side as the test point). So we analyze each option:

• Option 1: States that since \(0 \leq 2\) is true, we shade on the same side. This matches the rule for graphing linear inequalities (test point method).
• Option 2: Claims \(0 \leq 2\) is false, which is incorrect.
• Option 3: Says to shade on the opposite side when the test is true, which is incorrect (opposite side is for when the test is false).
• Option 4: Claims \(0 \leq 2\) is false (incorrect) and to shade opposite, which is doubly incorrect.

Answer:

A. Since \(0 \leq 2\) is TRUE, we must shade on the same side of the line.