Solving Systems of Equations 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 two lines to intersect?

Back

It means they have a common solution, which is the point where they meet.

Front

How do you find the solution to a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point of intersection.

Front

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

Back

(1, 3)

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have no solution because they never intersect.

Front

What is the significance of the point (0, 0) in a system of equations?

Back

It is the origin and can be a solution if it satisfies both equations.

Front

What is the graphical representation of the equation y = 3x - 2?

Back

A straight line with a slope of 3 and a y-intercept of -2.

Front

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

Back

Substitute the point's coordinates into both equations to see if they hold true.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

-2