24 - 25 FCMS A1 U4 CA TEST REVIEW

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What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

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What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

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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 variable.

Front

What is the Substitution Method in solving systems of equations?

Back

The Substitution Method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into both equations. If both equations are true, the point is a solution.

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What does it mean for a system of equations to have a unique solution?

Back

A system of equations has a unique solution if the graphs of the equations intersect at exactly one point.

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution if the graphs of the equations are parallel and never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

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A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the region that satisfies the inequality.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line in a linear inequality separates the solutions that satisfy the inequality from those that do not; a solid line indicates inclusion (≤ or ≥), while a dashed line indicates exclusion (< or >).