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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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What does it mean if a system of equations has one solution?

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It means the lines intersect at exactly one point, representing a unique solution for the variables.

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What does it mean if a system of equations has no solution?

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It means the lines are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

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What does it mean if a system of equations has infinitely many solutions?

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It means the equations represent the same line, so there are countless points that satisfy both equations.

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How can you determine if two equations are parallel?

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If their slopes are equal but their y-intercepts are different, the lines are parallel.

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What is the slope-intercept form of a linear equation?

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How do you find the solution to a system of equations graphically?

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Plot both equations on the same graph and identify the point(s) where the lines intersect.

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How do you identify the number of solutions from a graph?

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Count the number of intersection points of the lines: none (no solution), one (one solution), or infinitely many (same line).