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Questions and Answers
Which ordered pair is in the solution set of the system of linear inequalities: $y > \frac{3}{2} x - 1$ and $y < \frac{3}{2} x - 1$?
Which ordered pair is in the solution set of the system of linear inequalities: $y > \frac{3}{2} x - 1$ and $y < \frac{3}{2} x - 1$?
- (1, 1)
- (2, 2)
- No Solution (correct)
- (0, 0)
Which ordered pair makes both inequalities true: $y > -3x + 3$ and $y > 2x - 2$?
Which ordered pair makes both inequalities true: $y > -3x + 3$ and $y > 2x - 2$?
- (1, 4)
- (3, 5)
- (0, 0)
- (2, 2) (correct)
Which system of linear inequalities is represented by the graph?
Which system of linear inequalities is represented by the graph?
- $y > x - 2$ and $y < x + 1$ (correct)
- $y > -x + 3$ and $y < x + 1$
- $y < x - 2$ and $y < 2x + 1$
- $y < x + 2$ and $y > -2x + 1$
Which graph shows the solution to the system of linear inequalities: $x - 4y < 4$ and $y < x + 1$?
Which graph shows the solution to the system of linear inequalities: $x - 4y < 4$ and $y < x + 1$?
Which graph shows the solution to the system of linear inequalities: $y < 2x - 5$ and $y > -3x + 1$?
Which graph shows the solution to the system of linear inequalities: $y < 2x - 5$ and $y > -3x + 1$?
Which system of linear inequalities is represented by the graph?
Which system of linear inequalities is represented by the graph?
Which system of linear inequalities is represented by the graph?
Which system of linear inequalities is represented by the graph?
Which ordered pairs are in the solution set of the system of linear inequalities: $y > -\frac{1}{2} x$ and $y < \frac{1}{2} x + 1$?
Which ordered pairs are in the solution set of the system of linear inequalities: $y > -\frac{1}{2} x$ and $y < \frac{1}{2} x + 1$?
Which system of linear inequalities is represented by the graph?
Which system of linear inequalities is represented by the graph?
Which number completes the system of linear inequalities represented by the graph: $y > 2x - 2$ and $x + 4y > ?$?
Which number completes the system of linear inequalities represented by the graph: $y > 2x - 2$ and $x + 4y > ?$?
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Study Notes
Solving Systems of Linear Inequalities
- Evaluating ordered pairs helps determine if they belong to the solution set of a system of linear inequalities.
- For the inequalities ( y > \frac{3}{2} x - 1 ) and ( y < \frac{3}{2} x - 1 ), there is no solution.
- The ordered pair (2,2) satisfies the system ( y > -3x + 3 ) and ( y > 2x - 2 ).
Graph Interpretation
- A graph can visually represent systems of linear inequalities.
- The inequalities represented by the graph are ( y > x - 2 ) and ( y < x + 1 ).
- For the system defined by ( x - 4y < 4 ) and ( y < x + 1 ), the solution is depicted in a specific graph.
- The graph indicating ( y < 2x - 5 ) and ( y > -3x + 1 ) shows another solution set.
Additional Systems and Graphs
- The graph may represent the inequalities ( x + 5y > 5 ) and ( y < 2x + 4 ).
- For the inequalities ( y > x - 2 ) and ( x + 2y < 4 ), there is a corresponding graphical representation.
- A given system of inequalities where ( y > -\frac{1}{2} x ) and ( y < \frac{1}{2} x + 1 ) includes the ordered pairs (5, -2), (3, 1), and (4, 2).
Completing Systems
- The system characterized by ( y > \frac{1}{3} x + 3 ) and ( 3x - y > 2 ) can be interpreted from a graph.
- When completing the system involving ( y > 2x - 2 ), the equation can be completed with ( x + 4y > -12 ).
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