Algebra 1 Test Questions: Graphing Linear Inequality Systems

📚 Quick Study Guide

• 🧭 Definition: A system of linear inequalities is a set of two or more linear inequalities with the same variables.
• 📈 Graphing a Single Inequality:
  • ✏️ Graph the boundary line (replace the inequality sign with an equals sign). Use a solid line for $\leq$ or $\geq$, and a dashed line for $<$ or $>$.
  • 🧪 Choose a test point (not on the line) and plug it into the inequality.
  • 🎨 If the test point satisfies the inequality, shade the side of the line containing the test point. If not, shade the other side.
• 🧩 Graphing a System: Graph each inequality on the same coordinate plane. The solution to the system is the region where all shaded areas overlap.
• 🎯 Intersection: The overlapping region represents all points that satisfy all inequalities in the system.
• 💡 Tips:
  • 🧐 Use different colors or shading patterns for each inequality to easily identify the overlapping region.
  • ✍️ Always check your solution by picking a point in the overlapping region and verifying that it satisfies all inequalities.

Practice Quiz

1. Which of the following points is a solution to the system: $y > x + 1$ and $y < -x + 5$?

   1. (0, 0)
   2. (2, 2)
   3. (1, 4)
   4. (3, 1)

2. Which graph represents the solution to the system: $y \geq 2x - 3$ and $y \leq -x + 4$?

   1. [Imagine a graph where the region between y=2x-3 and y=-x+4 is shaded.]
   2. [Imagine a graph where the region above y=2x-3 and above y=-x+4 is shaded.]
   3. [Imagine a graph where the region below y=2x-3 and below y=-x+4 is shaded.]
   4. [Imagine a graph with no overlapping shaded region.]

3. Which inequality is represented by a dashed line on the graph?

   1. $y \geq x$
   2. $y \leq -x$
   3. $y > x + 2$
   4. $y = x - 1$

4. What does the overlapping shaded region in a system of linear inequalities represent?

   1. The set of points that satisfy only one inequality.
   2. The set of points that satisfy all inequalities.
   3. The set of points that satisfy none of the inequalities.
   4. The boundary lines of the inequalities.

5. Which system of inequalities corresponds to a graph where the overlapping region is in the first quadrant only?

   1. $x > 0$, $y > 0$
   2. $x < 0$, $y < 0$
   3. $x > 0$, $y < 0$
   4. $x < 0$, $y > 0$

6. If a point lies on a solid boundary line of an inequality, is it part of the solution?

   1. Yes, always.
   2. No, never.
   3. Yes, if the inequality includes "equal to".
   4. No, if the inequality includes "equal to".

7. Which of the following systems has no solution (no overlapping region)?

   1. $y > x$ and $y < x$
   2. $y > x$ and $y > -x$
   3. $y < x$ and $y < -x$
   4. $y > 2x$ and $y < 3x$