Solving Systems by Substitution and Elimination

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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 by substitution?

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Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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What does it mean to solve a system of equations by elimination?

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Solving by elimination 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?

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The substitution method is a technique for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method?

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The elimination method is a technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

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How do you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, meaning they have the same slope but different y-intercepts.

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How do you determine if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they have the same slope and y-intercept.

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

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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 solving a system of equations by elimination?

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The first step is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.

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The solution is (0, 1).