Review System of Equations (E-Learning 1/6)

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

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

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It means that the graphs of the equations intersect at exactly one point, indicating 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 that the graphs of the equations are parallel and never intersect, indicating that there is no set of values for the variables 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 that the equations represent the same line, so every point on the line is a solution to the system.

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How can you determine the number of solutions in a system of equations graphically?

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By graphing the equations and observing the number of intersection points: one point (one solution), no points (no solution), or infinitely many points (same line).

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the elimination method for solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

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What does it mean for two lines to be parallel?

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Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

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What does it mean for two lines to be perpendicular?

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Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.