Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method?

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

Front

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

Back

If a system has no solution, it means the equations represent parallel lines that never intersect.

Front

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

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If a system has infinitely many solutions, it means the equations represent the same line, and every point on that line is a solution.

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How do you determine if a system of equations is consistent or inconsistent?

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A system is consistent if it has at least one solution; it is inconsistent if it has no solutions.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection of the lines represented by the equations.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How can you identify the best method to solve a system of equations?

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The best method depends on the form of the equations; use substitution for easy-to-isolate variables, elimination for aligned coefficients, and graphing for visual solutions.