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 equations by elimination?

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It means to eliminate one variable by adding or subtracting the equations to find the value of the other variable.

Front

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

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The solution is the point where the lines intersect on a graph.

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

Back

It means there is no solution to the system, as the lines never intersect.

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

Back

It means there are infinite solutions, as the lines are the same.

Front

How do you determine the solution of a system of equations graphically?

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By plotting both equations on the same graph and identifying the intersection point.

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What is the substitution method in solving systems of equations?

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It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

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It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.