Systems of Equations

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What is a system of equations?

Back

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?

Back

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

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What is the substitution method?

Back

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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What is the elimination method?

Back

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

Front

What is a graphical solution to a system of equations?

Back

Finding the point(s) where the graphs of the equations intersect, which represents the solution(s) to the system.

Front

What does it mean if a system of equations has no solution?

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The lines representing the equations are parallel and never intersect.

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What does it mean if a system of equations has infinite solutions?

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The equations represent the same line, meaning every point on the line is a solution.

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How do you determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into each equation; if both equations are true, the point is a solution.

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What is the difference between consistent and inconsistent systems?

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Consistent systems have at least one solution, while inconsistent systems have no solutions.

Front

What is the graphical representation of a system of inequalities?

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The solution set is represented by a shaded region on the graph, indicating all possible solutions.