Solve Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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

Back

It means the equations represent parallel lines that never intersect.

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How can you determine if a system of equations has one solution?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines representing the equations.

Front

What is the substitution method in solving systems of equations?

Back

It 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?

Back

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

Front

What is the first step in graphing a system of equations?

Back

Convert each equation into slope-intercept form (y = mx + b) if necessary.

Front

What does the term 'consistent' mean in relation to systems of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

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What is the meaning of 'dependent' in systems of equations?

Back

Dependent equations are those that represent the same line, resulting in infinite solutions.