Solving Systems Using 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 using elimination?

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Solving 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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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, which means they never intersect.

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

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Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.

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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 (by multiplication or addition) to eliminate one variable.

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(-6, 7)

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(5, -8)

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(1, 7) is a solution.

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(0, 1)