Solving Systems of Equations and Inequalities Review

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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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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the graphical representation of a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

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

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The equations represent the same line, meaning every point on the line is a solution.

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How do you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify that both equations are satisfied.

Front

What is an inequality?

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A mathematical statement that compares two expressions, showing that one is less than, greater than, or not equal to the other.

Front

How do you graph a linear inequality?

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Graph the corresponding linear equation as a solid line (if ≤ or ≥) or dashed line (if < or >) and shade the appropriate region.