Solving Systems by 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 by elimination?

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Solving a system by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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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 removing one variable, allowing for the solution of the other variable.

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When can you use the elimination method?

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You can use the elimination method when the coefficients of one variable are opposites or can be made opposites through multiplication.

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What is the first step in the elimination method?

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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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What happens when you add two equations together?

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When you add two equations together, you can eliminate one of the variables if their coefficients are opposites.

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What is a coefficient in an equation?

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A coefficient is a numerical factor that multiplies a variable in an equation.

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

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A system has no solution if the equations represent parallel lines that never intersect.

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What does it mean 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 every point on the line is a solution.

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How do you determine if a system is ready to be solved by elimination?

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A system is ready to be solved by elimination if you can manipulate the equations to eliminate one variable.