Creating and Solving Systems of Equations/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 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 on a graph.

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What does it mean for a solution to be feasible in a system of inequalities?

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A feasible solution is a solution that satisfies all the inequalities in the system.

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How can you graph a system of inequalities?

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1. Graph each inequality as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is the graphical method for solving systems of equations?

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The graphical method involves plotting both equations on a graph and identifying the point(s) where they intersect.

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What is the meaning of 'consistent' in a system of equations?

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

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What is the meaning of 'inconsistent' in a system of equations?

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An inconsistent system has no solutions, meaning the equations do not intersect at any point.