Unit 4 Review - 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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

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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 equations represent parallel lines that 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 any 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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What is the significance of the point of intersection in a system of equations?

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The point of intersection represents the solution to the system, where the values of the variables satisfy all equations.

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or dashed line (for < or >). 2. Shade the region that satisfies the inequality.