Solving Systems of Linear Equations

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What is a system of linear equations?

Back

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?

Back

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

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What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

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What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for a variable and substituting that expression into the other equation.

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What does it mean if a system 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 has one solution?

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The lines represented by the equations intersect at exactly one point.

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

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The lines represented by the equations are the same line, meaning they intersect at every point on that line.

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How do you determine the number of solutions in a system of equations?

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By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

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

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The solution is represented by the point(s) where the lines intersect on a graph.

Front

What is the first step in the elimination method?

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Align the equations so that corresponding variables and constants are in the same columns.