System of Equations and Inequalities

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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.

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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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What is the graphical representation of a system of equations?

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The graphical representation is the intersection point(s) of the lines representing each equation.

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What does it mean for a system of equations to be consistent?

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A consistent system has at least one solution, meaning the lines intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system has no solutions, meaning the lines are parallel and never intersect.

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap.

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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.

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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 the equations are satisfied, the point is a solution.