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 on a graph.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations consists of the lines or curves of each equation plotted on the same coordinate plane.

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What is the solution of a system of equations represented graphically?

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The solution of a system of equations is represented by the point(s) where the graphs of the equations intersect.

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What is the substitution method in 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 in 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 does it mean if a system of equations has no solution?

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A system of equations has no solution if the lines representing the equations are parallel and never intersect.

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

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A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

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How can you determine the solution of a system of equations algebraically?

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You can determine the solution algebraically by using methods such as substitution or elimination to find the values of the variables.

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What is a consistent system of equations?

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A consistent system of equations is one that has at least one solution, meaning the equations intersect at one or more points.