Unit 4 Review - Systems of Equations

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

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

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It means that the lines represented by the equations are parallel and will never intersect.

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What does it mean if a system of equations has an infinite number of 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 by 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 by 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 one 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. The intersection points represent the solutions.

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One solution, since the lines intersect at a single point.

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x = 2.

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x = 5.

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What does it mean if two equations are dependent?

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It means they represent the same line, resulting in an infinite number of solutions.