Systems of Linear Equations

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What is a system of linear equations?

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A set of two or more linear equations with the same variables. Solutions are the points where the equations intersect.

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What does it mean to solve a system of linear equations?

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Finding the values of the variables that satisfy all equations in the system simultaneously.

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What are the three methods to solve a system of linear equations?

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1. Graphing 2. Substitution 3. Elimination

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What is the graphical representation of a system of linear equations?

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The lines representing each equation on a coordinate plane, where the intersection point(s) represent the solution(s).

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

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The lines are parallel and do not intersect, indicating that there are no values that satisfy all equations.

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What does it mean if a system of linear equations has an infinite number of solutions?

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The equations represent the same line, meaning every point on the line is a solution.

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How do you determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into each equation. If all equations are satisfied, the point is a solution.

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What is the substitution method for solving systems of equations?

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Solve one equation for one variable and substitute that expression into the other equation.

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What is the elimination method for solving systems of equations?

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Add or subtract equations to eliminate one variable, making it easier to solve for the remaining variable.

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How can you represent a system of equations using matrices?

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By creating a coefficient matrix and a constant matrix, which can be solved using matrix operations.