System of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

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What does it mean if a system of equations has one solution?

Back

It means that the lines representing the equations cross at exactly one point.

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

Back

It means that the lines representing the equations are the same, or coincide.

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How can you determine if a system of equations has no solution?

Back

If the lines representing the equations are parallel, they will never intersect, indicating no solution.

Front

What is the graphical representation of a system of equations with one solution?

Back

The graphical representation shows two lines that intersect at a single point.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The graphical representation shows two lines that lie on top of each other.

Front

What is the graphical representation of a system of equations with no solution?

Back

The graphical representation shows two parallel lines that never intersect.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method in solving systems of equations?

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The elimination method 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 consistent system has at least one solution, which can be either one solution or infinitely many solutions.