Systems of Equations (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 elimination mean in the context of solving systems of equations?

Back

Elimination is a method for solving systems of equations by removing one variable, allowing for the solution of the remaining variable.

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How do you eliminate a variable in a system of equations?

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To eliminate a variable, you can add or subtract the equations after multiplying them by suitable coefficients to make the coefficients of one variable equal.

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 decide which variable to eliminate.

Front

Solve the system of equations by elimination: 5x + 7y = -17 and -8x + 7y = 9.

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(-2, -1)

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Solve the system of equations by elimination: x + 6y = -16 and -x - 9y = 19.

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(-10, -1)

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Solve the system of equations by elimination: -8x - 6y = -12 and -8x - 8y = 8.

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(9, -10)

Front

Solve the system of equations by elimination: 7x + 9y = 25 and -7x - 5y = -17.

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(1, 2)

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What does it mean if a system of equations has an infinite number of solutions?

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It means that the equations represent the same line, and every point on that line is a solution.

Front

Solve the system of equations by elimination: 6x - 6y = 24 and 6x - 6y = 24.

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Infinite number of solutions