Systems of Equations - Recap

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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.

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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 substitution method?

Back

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?

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

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What does it mean to create opposites in a system of equations?

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Creating opposites means manipulating the equations so that one variable cancels out when the equations are added or subtracted.

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What is the first step in using the substitution method?

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The first step is to solve one of the equations for one variable in terms of the other variable.

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What is the first step in using the elimination method?

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The first step is to align the equations and manipulate them (if necessary) so that the coefficients of one variable are opposites.

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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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How can you check the solution of a system of equations?

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You can check the solution by substituting the values back into the original equations to see if they hold true.

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What is a consistent system of equations?

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