Solving Systems by 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 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 other variable.

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What is the elimination method?

Back

The elimination method is a technique used to solve systems of equations by removing one variable, allowing for the other variable to be solved directly.

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How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

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If the lines intersect at one point, there is one solution. If the lines are parallel, there is no solution. If the lines coincide, there are infinitely many solutions.

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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 so that corresponding variables and constants are in the same columns.

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How can you make the coefficients of one variable the same in both equations?

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You can multiply one or both equations by a number to make the coefficients of one variable equal.

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What is the solution to the system: 2x + 9y = -7 and 6x - 3y = 9?

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(1, -1)

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What is the solution to the system: 4x + 9y = 28 and -4x - y = -28?

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(7, 0)

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How do you write a system of equations from a word problem?

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Identify the variables, translate the relationships into equations, and set them equal to each other based on the problem's context.

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What is the solution to the system: 2x + 3y = 12 and 5x - y = 13?

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(3, 2)