Solving systems of linear equations involves finding the values of variables that satisfy all equations in the system simultaneously. This can be done using methods such as substitution, elimination, or graphing.
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A system of linear equations can have one solution, no solution, or infinitely many solutions.
The graphical representation of a system with two variables is two lines that can intersect (one solution), be parallel (no solution), or coincide (infinitely many solutions).
The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.
The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.
Systems of linear equations can also be solved using matrices and determinants.
Review Questions
What are the possible outcomes when solving a system of two linear equations?
Describe the substitution method for solving systems of linear equations.
How does the elimination method work in solving a system of linear equations?
Related terms
Substitution Method: A technique for solving systems of equations by expressing one variable in terms of another and substituting this expression into another equation.
Elimination Method: A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.
Matrix: A rectangular array of numbers arranged in rows and columns used to represent a system of linear equations.
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