Systems of equations and inequalities

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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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How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

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

Back

A point is a solution if it satisfies all equations in the system.

Front

What is the graphical representation of a system of inequalities?

Back

The solution is represented by the shaded region where all inequalities overlap.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

What is the difference between a solution to an equation and a solution to an inequality?

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An equation has a specific solution, while an inequality has a range of solutions.

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What does it mean to graph a system of equations?

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It means to plot each equation on the same coordinate plane and find the intersection points.

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What is the substitution method?

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A method for solving systems of equations by expressing one variable in terms of the other.

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What is the elimination method?

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A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

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What is a feasible region in the context of inequalities?

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The area on a graph where all constraints of the inequalities are satisfied.