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 graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What is the solution to a system of equations?

Back

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

Front

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

Back

It indicates that there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines coincide when graphing?

Back

It means that there are infinite solutions, as every point on the line is a solution to the system.

Front

How do you determine the solution from a graph?

Back

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

Front

What is the significance of the y-intercept in a linear equation?

Back

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

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of the line, calculated as the rise over run (change in y over change in x).

Front

How can you tell if a system of equations has one solution?

Back

If the lines representing the equations intersect at exactly one point.

Front

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

Back

It represents a straight line where m is the slope and b is the y-intercept.