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 for a solution to a system of equations?

Back

An ordered pair that satisfies all equations in the system.

Front

How can you graphically represent a system of linear equations?

Back

By plotting each equation on the same coordinate plane and finding the intersection point.

Front

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.

Front

What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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What does it mean if two lines are parallel in a system of equations?

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The system has no solution because the lines never intersect.

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What does it mean if two lines coincide in a system of equations?

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The system has infinitely many solutions because the lines are the same.

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How do you determine if a system of equations has a unique solution?

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If the lines intersect at exactly one point, the system has a unique solution.

Front

Solve the system: 2x + 3y = 6 and x - y = 1.

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(3,0) is the solution.

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Solve the system: y = 3x + 2 and y = -x + 4.

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(1,5) is the solution.