WU: Solving Systems by Graphing

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 to have no solution?

Back

It means the lines representing the equations are parallel and never intersect.

Front

What does it mean for a system to have one solution?

Back

It means the lines intersect at exactly one point, which is the solution to the system.

Front

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

Back

It means the lines are coincident, lying on top of each other, representing the same line.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the solution.

Front

What is the graphical representation of the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope is 3.

Front

What is the y-intercept of the line represented by the equation y = -2x + 5?

Back

The y-intercept is 5.

Front

How can you determine if a system of equations has no solution by looking at their graphs?

Back

If the lines are parallel, the system has no solution.