Alg 2 Practice Flashcard 1.5-1.7

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What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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

Back

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

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What does it mean if a system of equations has infinite solutions?

Back

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What is the graphical representation of a system of inequalities?

Back

The graphical representation of a system of inequalities is the shaded region on a graph that satisfies all inequalities. The boundaries are often dashed or solid lines depending on whether the inequalities are strict (<, >) or inclusive (≤, ≥).

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How do you solve a system of equations using subtraction?

Back

To solve a system of equations using subtraction, align the equations and subtract one from the other to eliminate one variable, making it easier to solve for the remaining variable.

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What is the solution to the system of equations: 2x + y = 10 and 2x - 3y = 6?

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The solution is x = 4.5 and y = 1.

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What is a solution to a system of inequalities?

Back

A solution to a system of inequalities is any point (x, y) that satisfies all inequalities in the system.

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

Back

Substitute the point into each inequality. If it satisfies all inequalities, it is a solution.

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What does it mean if a point lies outside the shaded region of a graph representing a system of inequalities?

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If a point lies outside the shaded region, it does not satisfy the system of inequalities and is not a solution.