Solving 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 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 are the three methods to solve systems of equations?

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1. Graphing 2. Substitution 3. Elimination

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What is the substitution method?

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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?

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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 if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have no points of intersection, and thus, the system has no solution.

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What does it mean if two lines coincide in a system of equations?

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If two lines coincide, they lie on top of each other, meaning there are infinitely many solutions to the system.

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How do you determine the solution of a system of equations graphically?

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The solution is the point where the graphs of the equations intersect.

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

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Isolate one variable in one of the equations.

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

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Align the equations and manipulate them to eliminate one variable.