Systems of Equations Elimination (Easy)

Front

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 set of values that satisfy all equations simultaneously.

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What does it mean for a system of equations to have no solution?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

How do you determine if two equations are dependent?

Back

Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and manipulate them (if necessary) so that the coefficients of one variable are opposites.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system of equations is inconsistent if there is no solution, typically when the equations represent parallel lines.

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How can you check your solution for a system of equations?

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You can check your solution by substituting the values back into the original equations to see if they hold true.

Front

What is the significance of the coefficients in a system of equations?

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The coefficients determine the slope and position of the lines represented by the equations, affecting their intersection and solution.

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What is a unique solution in the context of systems of equations?

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A unique solution occurs when the equations intersect at exactly one point, meaning there is one set of values for the variables.

Front

How do you solve for one variable using the elimination method?

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To solve for one variable, you can add or subtract the equations to eliminate the other variable, then solve the resulting equation.