Systems of Equations and Inequalities

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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 for a system of equations to have one solution?

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It means that the graphs of the equations intersect at exactly one point.

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What does it mean for a system of equations to have no solution?

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It means that the graphs of the equations are parallel and never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

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It means that the equations represent the same line, so every point on the line is a solution.

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How do you solve a system of equations using substitution?

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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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How do you solve a system of equations using elimination?

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1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable.

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What is the graphical representation of a system of equations?

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The graphical representation consists of the lines of the equations plotted on a coordinate plane.

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The solution is (3, 2).

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Yes, it is a solution.

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The point (1, 0) is a solution.