Systems of Equations Graphing (Math)

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 solution?

Back

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

Front

What does the graph of a system of equations represent?

Back

The graph represents the relationships between the variables and the solutions to the equations.

Front

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

Back

(1, 3)

Front

What does it mean if two lines intersect on a graph?

Back

It means the system of equations has one unique solution.

Front

What does it mean if two lines are parallel on a graph?

Back

It means the system of equations has no solution.

Front

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

Back

The lines overlap completely on the graph.

Front

How can you determine the solution to a system of equations graphically?

Back

By finding the point where the lines intersect on the graph.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = 3x + 2?

Back

2, which is the point (0, 2) on the graph.