solve 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 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?

Back

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

Front

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

Back

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

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines: same slope and intercept = infinite solutions, same slope different intercept = no solution, different slopes = one solution.

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

How do you find the intersection point of two lines graphically?

Back

By plotting both lines on the same graph and identifying the point where they cross.

Front

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

Back

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

Front

What does it mean if a system has one solution?

Back

It means the lines intersect at exactly one point, providing a unique solution for the variables.