Systems of Equations: Elimination

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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 elimination mean in the context of 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?

Back

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?

Back

The first step is to align the equations and decide which variable to eliminate.

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

Back

Infinite number of solutions.

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Solve by elimination: 3x + 2y = 12 and 3x - 4y = 0. What is the solution?

Back

(4, 0)

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What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

Back

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

Front

Solve by elimination: 5x + 2y = 10 and 5x - 2y = 0. What is the solution?

Back

(2, 0)

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What is the elimination method used for?

Back

The elimination method is used to find the values of variables that satisfy all equations in a system.