Systems of Equations Review

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 for a system of equations to have one solution?

Back

It means that the equations intersect at exactly one point on the graph.

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What does it mean for a system of equations to have no solutions?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are satisfied, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines or curves of the equations plotted on a coordinate plane.

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What is the substitution method for solving systems of equations?

Back

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 for solving systems of equations?

Back

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

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations.

Front

How do you identify parallel lines in a system of equations?

Back

Parallel lines have the same slope but different y-intercepts.