Systems of Equations by Substitution and Elimination

Front

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 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.

Front

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.

Front

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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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 never intersect.

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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 overlap completely.

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What is the substitution method used for?

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The substitution method is used to solve systems of equations by expressing one variable in terms of the other and substituting it into the second equation.

Front

What is the elimination method used for?

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The elimination method is used to solve systems of equations by eliminating one variable to solve for the other.

Front

Solve the system by substitution: x - 3y = -13 and 4x + 2y = 4. What is the solution?

Back

(-1, 4)

Front

Solve the system by elimination: -3x - 6y = 24 and 4x + 4y = 4. What is the solution?

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(10, -9)