Solving 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.

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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 is the graphical representation of a system of linear equations?

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The intersection point(s) of the lines represented by the equations.

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What is the elimination method in solving systems of equations?

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A method that involves adding or subtracting equations to eliminate one variable.

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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

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The lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many 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 solution is correct for a system of equations?

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Substitute the solution back into the original equations to see if they hold true.

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What is the first step in solving a system of equations by elimination?

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Align the equations so that like terms are in the same column.

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What is the first step in solving a system of equations by substitution?

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Solve one of the equations for one variable in terms of the other.