Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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

Back

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

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

Back

It means the equations represent parallel lines that never intersect.

Front

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

Back

It means the equations represent the same line (coinciding lines) on the graph.

Front

How can you determine if a system of equations has a unique solution?

Back

By checking if the lines represented by the equations intersect at one point.

Front

What is the graphical representation of intersecting lines?

Back

Two lines that cross each other at one point.

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What is the graphical representation of parallel lines?

Back

Two lines that run alongside each other and never meet.

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What is the graphical representation of coinciding lines?

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Two lines that lie on top of each other, representing the same equation.

Front

How do you solve a system of equations using substitution?

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By solving one equation for a variable and substituting that expression into the other equation.

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How do you solve a system of equations using elimination?

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By adding or subtracting equations to eliminate one variable, making it easier to solve for the other.