Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. Solutions are the points where the equations intersect.

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

Back

A point is a solution if it satisfies all equations in the system, meaning it makes all equations true.

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How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If all equations are satisfied, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane. Solutions are the intersection points.

Front

What are the possible outcomes when solving a system of equations graphically?

Back

1. One solution (intersecting lines), 2. No solution (parallel lines), 3. Infinitely many solutions (same line).

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What is 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 is elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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What does it mean if two equations are dependent?

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Dependent equations have infinitely many solutions; they represent the same line.

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What does it mean if two equations are independent?

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Independent equations have exactly one solution; they represent two intersecting lines.

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What does it mean if two equations are inconsistent?

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Inconsistent equations have no solutions; they represent parallel lines that never intersect.