Systems of Equations 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 graph a system of equations?

Back

It means to plot the equations on a coordinate plane to find their intersection point.

Front

What is the solution to a system of equations?

Back

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

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

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: if they are the same, there are infinitely many solutions; if they are different, there is one solution; if they are parallel, there is no 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 a 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 is the slope of a line?

Back

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