Solving Systems of Equations

Front

What is a system of equations?

Back

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

Front

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

Back

It means the lines intersect at exactly one point.

Front

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

Back

It means the lines are parallel and never intersect.

Front

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

Back

It means the lines coincide, or are the same line.

Front

How do you solve a system of equations graphically?

Back

By plotting the equations on a graph and finding the intersection point.

Front

What is the substitution method?

Back

A method where you solve one equation for one variable and substitute it into the other equation.

Front

What is the elimination method?

Back

A method where you add or subtract equations to eliminate one variable.

Front

What is the point of intersection in a graph of two lines?

Back

It is the solution to the system of equations represented by those lines.

Front

If y = 2x + 3 and y = -x + 1, what is the solution?

Back

(1, 5)

Front

What is the slope of a line?

Back

The slope is the ratio of the rise (change in y) to the run (change in x).