System of Equations Unit Review

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

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How do you represent a system of equations graphically?

Back

A system of equations can be represented graphically by plotting each equation on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

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

Back

A consistent system of equations has at least one solution. It can be either independent (one solution) or dependent (infinitely many solutions).

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

Back

An inconsistent system of equations has no solutions. This occurs when the equations represent parallel lines that never intersect.

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What is the substitution method for solving a system of equations?

Back

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

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What is the elimination method for solving a system 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 remaining variable.

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How can you check if a solution is correct for a system of equations?

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To check if a solution is correct, substitute the values back into the original equations. If both equations are satisfied, the solution is correct.

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What is the graphical interpretation of the solution to a system of equations with one solution?

Back

The graphical interpretation is that the two lines intersect at exactly one point, which represents the unique solution to the system.

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What is the graphical interpretation of the solution to a system of equations with infinitely many solutions?

Back

The graphical interpretation is that the two lines coincide, meaning they are the same line, resulting in infinitely many solutions.

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What is the graphical interpretation of the solution to a system of equations with no solution?

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The graphical interpretation is that the two lines are parallel and never intersect, indicating that there is no solution.