Linear Systems
Solve systems of equations and inequalities using graphs and algebra.
Two Constraints
Graph of a System
Solution to a System
Graphing Constraints
Building a System
Level Check
Graphing Systems of Equations
Slope-Intercept and Systems
Point-Slope and Systems
Approximate Solutions
Systems with No Solution
Systems with Infinitely Many Solutions
Level Check
Solve by Substituting
Isolating to Substitute
Adding Equations
Scaling an Equation
Scaling Both Equations
Two Inequality Constraints
Graphing a System of Inequalities
Building a System of Inequalities
Interpreting Solutions
Reading Graphs
Representing Solutions
Graphing Systems
Special Systems of Inequalities
Course description
In this course, you'll learn to solve systems of two linear equations by exploring situations where two constraints must be satisfied at the same time. You'll start by interpreting real-world scenarios with two unknowns, then move to graphing lines and finding their intersection. You'll solve systems algebraically using substitution and elimination, and learn to recognize when a system has no solution or infinitely many solutions. Finally, you'll extend these ideas to systems of inequalities, identifying and graphing the regions where multiple constraints overlap.
Topics covered
- Writing equations for constraints
- Graphing systems of equations
- Finding solutions as intersection points
- Graphing lines using slope-intercept form
- Graphing lines using point-slope form
- Estimating approximate solutions
- Identifying systems with no solution
- Identifying systems with infinitely many solutions
- Solving systems by substitution
- Solving systems by elimination
- Scaling equations to eliminate variables
- Writing systems of inequalities
- Graphing systems of inequalities
- Interpreting solution regions