Systems of Equations - Review

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What is a system of equations?

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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.

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

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A system has one solution when the graphs of the equations intersect at exactly one point.

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

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A system has no solution when the graphs of the equations are parallel and never intersect.

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

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A system has infinite solutions when the equations represent the same line, meaning they intersect at every point on that line.

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How do you solve a system of equations using substitution?

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To solve by substitution, solve one equation for one variable, then 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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To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

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What is the graphical representation of a system of equations?

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The graphical representation consists of the lines of the equations plotted on a coordinate plane.

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What is the significance of the point of intersection in a system of equations?

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The point of intersection represents the solution to the system, indicating the values of the variables that satisfy all equations.

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What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A is non-negative.

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How can you determine the number of solutions from a graph?

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Count the number of intersection points of the lines: one point means one solution, no points means no solution, and overlapping lines mean infinite solutions.