Solving systems of linear equations involves finding the values of variables that satisfy all equations in the system simultaneously. Typically, these systems can be solved using methods such as graphing, substitution, or elimination.
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A system of linear equations can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (coinciding lines).
The substitution method involves solving one equation for a variable and substituting this expression into another equation.
The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.
Graphing is a visual method where the point(s) of intersection represent the solution(s) to the system.
Systems of linear equations can also be represented and solved using matrices.
Review Questions
What are three common methods used to solve systems of linear equations?
How can you determine if a system of linear equations has no solution by graphing?
Explain how the elimination method works in solving a system of linear equations.
Related terms
Substitution Method: A technique for solving systems of linear equations by solving one equation for one variable and substituting this value into another equation.
Elimination Method: A technique for solving systems of linear equations by adding or subtracting equations to eliminate a variable and simplify the system.
Matrix: A rectangular array of numbers arranged in rows and columns that can represent a system of linear equations.
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