Linear Equations and Inequalities Sheet
Unit 3 - Systems of Equations
Lesson 1 - Systems of 2 Variables
Review - Linear Equations & Graphs
Example 1 \(y = \frac{1}{2}x - 2\)
x y -5 5 -5 5
Example 2 \(2x + 3y = 6\)
x y -5 5 -5 5
Example 3 \(2x - y = 4\)
x y -5 5 -5 5
Unit 3 - Systems of Equations
Lesson 1 - Systems of 2 Variables
Systems of Linear Inequalities - Notes
Shades Up \(y > \frac{1}{2}x + 1\)
Shades Down \(\frac{1}{2}x + 1 > y\)
Example 1 System of 2 Inequalities
\(2x + y\) \(\le\) \(4\)
\(y\) \(\le\) \(-2x + 4\)
\(x - 2y\) \( < \) \(2\)
\(y\) \( > \) \(\frac{1}{2}x - 1\)
Example 2 System of 3 Inequalities
\(y\) \(\ge\) \(-1\)
\(x + y\) \( < \) \(3\)
\(y\) \( < \) \(-x + 3\)
\(2x - y\) \(\ge\) \(-3\)
\(y\) \(\le\) \(2x + 3\)
Example 3 System of 3 Inequalities
No Solution (\(\emptyset\))
\(x + y\) \( > \) \(3\)
\(y\) \( > \) \(-x + 3\)
\(x + y\) \( < \) \(-1\)
\(y\) \( < \) \(-x - 1\)
\(2x - y\) \(\le\) \(2\)
\(y\) \(\ge\) \(2x - 2\)
Linear Inequalities Practice Worksheet
Unit 3 - Systems of Equations
Lesson 1 - Systems of 2 Variables
Linear Equations & Inequalities Practice
Name:
Part 1: Linear Equations Graph each equation
1 \(y = -\frac{1}{2}x + 2\)
x y -5 5 -5 5
\(y\)-int:
Slope (\(m\)):
2 \(3x + 2y = 6\)
x y -5 5 -5 5
\(y\)-int:
Slope (\(m\)):
3 \(x - 2y = 4\)
x y -5 5 -5 5
\(y\)-int:
Slope (\(m\)):
Part 2: Linear Inequalities Graph & shade half-plane
4 \(y > \frac{1}{2}x - 2\)
x y -5 5 -5 5
\(y\)-int:
Slope (\(m\)):
Boundary: Solid / Dashed
Shade: Above / Below
5 \(2x + 3y \le 6\)
x y -5 5 -5 5
\(y\)-int:
Slope (\(m\)):
Boundary: Solid / Dashed
Shade: Above / Below
6 \(3x - 2y \ge 6\)
x y -5 5 -5 5
\(y\)-int:
Slope (\(m\)):
Boundary: Solid / Dashed
Shade: Above / Below
Unit 3 - Systems of Equations
Lesson 1 - Systems of 2 Variables
Systems of Linear Inequalities Practice
Graph and shade each feasible solution region
7 System of 2 Inequalities
\(x + y \le 3\)
\(y \le\)
Line: Solid / Dashed
Shade: Above / Below
\(2x - y < 4\)
\(y\)
Line: Solid / Dashed
Shade: Above / Below
x y -5 5
8 System of 3 Inequalities
\(y \ge -2\)
Horizontal line
Line: Solid / Dashed
Shade: Above / Below
\(x - y \le 1\)
\(y\)
Line: Solid / Dashed
Shade: Above / Below
\(2x + y \le 4\)
\(y\)
Line: Solid / Dashed
Shade: Above / Below
x y -5 5
9 System of 3 Inequalities
\(x + 2y \ge -2\)
\(y\)
Line: Solid / Dashed
Shade: Above / Below
\(x - 2y \le 6\)
\(y\)
Line: Solid / Dashed
Shade: Above / Below
\(x \le 2\)
Vertical line
Line: Solid / Dashed
Shade: Left / Right
x y -5 5
10 System of 4 Inequalities
\(x + y \le 4\)
Line: Solid / Dashed
Shade: Above / Below
\(x - y \le 2\)
Line: Solid / Dashed
Shade: Above / Below
\(x \ge 0\)
Line: Solid / Dashed
Shade: Left / Right
\(y \ge 0\)
Line: Solid / Dashed
Shade: Above / Below
x y -5 5
