Solving Systems by Graphing

Front

What is a system of linear equations?

Back

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

Front

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

Back

They have no solutions because they never intersect.

Front

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

Back

They have infinitely many solutions because they overlap completely.

Front

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

Back

They have exactly one solution, which is the point of intersection.

Front

How do you graph a linear equation?

Back

By plotting points that satisfy the equation and connecting them with a straight line.

Front

What is the solution to the system of equations represented graphically?

Back

The point where the lines intersect.

Front

What is the significance of the coordinates in a solution (x, y)?

Back

They represent the values of the variables that satisfy both equations.

Front

If a system of equations has no solution, what can be said about the lines?

Back

The lines are parallel.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

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

Back

By substituting the point's coordinates into both equations and checking for equality.