Solving System of Equations

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system of equations?

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Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the elimination method?

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A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

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How do you use the elimination method?

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1. Align the equations. 2. Multiply equations if necessary to match coefficients. 3. Add or subtract equations to eliminate one variable. 4. Solve for the remaining variable.

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What is substitution method?

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A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

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How do you use the substitution method?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.

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What is a dependent system of equations?

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A system that has infinitely many solutions, where the equations represent the same line.

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What is the graphical method of solving systems of equations?

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Plotting the equations on a graph and identifying the point(s) where they intersect.