Elimination method

Front

What is the Elimination Method in solving systems of equations?

Back

The Elimination Method is a technique used to solve systems of linear equations by eliminating one variable, allowing for the solution of the other variable.

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How do you eliminate a variable in the Elimination Method?

Back

To eliminate a variable, you can multiply one or both equations by a number so that the coefficients of one variable are opposites, allowing you to add or subtract the equations.

Front

What is the first step in using the Elimination Method?

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

Front

Solve using Elimination Method: x - y = 11 and 2x + y = 19. What is the solution?

Back

(10, -1)

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Solve for x using Elimination Method: 4x + 9y = 28 and -4x - y = -28. What is the solution?

Back

(7, 0)

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

Back

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

Front

Solve the system: x + 6y = 17 and -x + 3y = -8. What is the solution?

Back

(11, 1)

Front

What is the significance of the coefficients in the Elimination Method?

Back

The coefficients determine how the equations can be manipulated to eliminate a variable.

Front

Solve by elimination: 7x - 9y = 29 and 7x + 2y = -15. What is the solution?

Back

(-1, -4)

Front

What is a consistent system of equations?

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A consistent system has at least one solution, meaning the lines intersect at one or more points.