Systems of Linear Equations Fundamentals
Master key concepts and methods for solving systems in two and three variables.
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Questions Covered in This Set
8 cards to master
What is a system of linear equations?
A collection of two or more linear equations that we solve simultaneously to find values that make all equations true at the same time.
Describe the substitution method for solving systems.
Solve one equation for one variable, then substitute that expression into the other equation to eliminate a variable and solve.
Describe the elimination method for solving systems.
Add or subtract equations (after multiplying if needed) to eliminate one variable, then solve for the remaining variable.
What does an inconsistent system mean?
A system with no solution because the lines or planes never meet (parallel), resulting in contradictions like 0 = 5.
What does a dependent system mean?
A system with infinitely many solutions because the equations describe the same line or plane, resulting in identities like 0 = 0.
What do three-variable systems represent geometrically?
Planes in three-dimensional space, where the solution is the point where all three planes intersect.
When is substitution the best method to use?
When one variable is already isolated or can be easily isolated in one of the equations.
What is the first step in solving a three-variable system using elimination?
Choose one variable to eliminate first, then use pairs of equations to create two new equations without that variable.
