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 to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

It means there is no solution, as the lines never intersect.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

It means there are infinitely many solutions, as the lines overlap completely.

Front

How can you determine the solution from a graph?

Back

By identifying the coordinates of the intersection point of the lines.

Front

What is the significance of the x-intercept in a graph?

Back

It is the point where the graph crosses the x-axis, indicating the value of x when y=0.

Front

What is the significance of the y-intercept in a graph?

Back

It is the point where the graph crosses the y-axis, indicating the value of y when x=0.

Front

What does it mean if a system of equations has one solution?

Back

It means the lines intersect at exactly one point.

Front

What is the graphical representation of the equation y = mx + b?

Back

It represents a straight line with slope m and y-intercept b.