Solving Systems of Equations 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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The equations are represented as lines on a graph, and the solution is the point where the lines intersect.

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What does it mean if two lines are parallel in a system of equations?

Back

It means the system has no solution because the lines never intersect.

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What does it mean if two lines coincide in a system of equations?

Back

It means the system has infinitely many solutions because the lines overlap completely.

Front

How do you solve a system of equations using substitution?

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You solve one equation for one variable and substitute that expression into the other equation.

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How do you solve a system of equations using elimination?

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You add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the solution to the system of equations x + y = 5 and x - y = 1?

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(3, 2) is the solution.

Front

What is the substitution method?

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A method for solving systems of equations by expressing one variable in terms of the other.

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What is the elimination method?

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A method for solving systems of equations by adding or subtracting equations to eliminate a variable.