System of Equations Review

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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 represent a system of equations graphically?

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Graphically, a system of equations is represented by the lines of the equations on a coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

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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. It can be either independent (one solution) or dependent (infinitely many solutions).

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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 representing the equations are parallel and never intersect.

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How do you solve a system of equations using substitution?

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To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

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How do you solve a system of equations using elimination?

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To solve by elimination, manipulate the equations to eliminate one variable, allowing you to solve for the other variable.

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What is the graphical representation of the inequality y < mx + b?

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The graph of y < mx + b is a dashed line representing the boundary, with the solution set being the area below the line.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (> or <).

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What does the solution set of a system of inequalities represent?

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The solution set of a system of inequalities represents all the points that satisfy all inequalities in the system, often depicted as a shaded region on a graph.

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How can you check if a point is a solution to a system of inequalities?

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To check if a point is a solution, substitute the point's coordinates into each inequality. If it satisfies all inequalities, it is a solution.