solving Systems (elimination, substitution)

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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 other variable.

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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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How do you determine which method to use for solving a system of equations?

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Consider the coefficients of the variables; if one variable has a coefficient of 1 or -1, substitution may be easier. If the coefficients are easily manipulated to cancel out, elimination may be quicker.

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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 that are solved simultaneously.

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What does it mean for a system of equations to be consistent?

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

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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What is the graphical representation of a system of equations?

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The graphical representation involves plotting each equation on a coordinate plane and identifying the points of intersection.

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How can you check your solution to a system of equations?

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Substitute the solution back into the original equations to verify that both equations are satisfied.

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What is the first step in solving a system of equations using elimination?

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Align the equations and manipulate them (if necessary) to ensure that the coefficients of one variable are opposites.

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What is the first step in solving a system of equations using substitution?

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Solve one of the equations for one variable in terms of the other variable.