Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

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

Back

It means there are no values for the variables that can satisfy all equations in the system.

Front

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

Back

It means there are countless sets of values for the variables that satisfy all equations in the system.

Front

What is the graphical representation of a system with a unique solution?

Back

Two lines that intersect at one point.

Front

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

Back

Two parallel lines that never intersect.

Front

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

Back

Two lines that coincide, or are the same line.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the y-intercept of the equation y = -x + 5?

Back

The y-intercept is 5.