Solving Systems Algebraically

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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 for a system of equations to have a unique solution?

Back

It means that the equations intersect at exactly one point on a graph.

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

Back

It means that the equations represent parallel lines that never intersect.

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How do you solve a system of equations algebraically?

Back

You can use substitution or elimination methods to find the values of the variables.

Front

What is the substitution method?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

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What is the elimination method?

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A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

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What is the graphical representation of a system of equations?

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It is represented by the graphs of the equations on the same coordinate plane.

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What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where the values of the variables satisfy all equations.

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

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Substitute the values back into the original equations to see if they hold true.