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 for two lines to intersect on a graph?

Back

It means that the two equations have a common solution, represented by the point of intersection.

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 parallel, there is no solution; if they are the same line, there are infinitely many solutions; if they intersect, there is 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 graph the equation y = 2x?

Back

Start at the origin (0,0), use the slope of 2 to rise 2 units up for every 1 unit you move right.

Front

What is the solution to the system of equations y = 2x and y = 3x + 1?

Back

(-1, -2), the point where the two lines intersect.

Front

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

Back

It means the lines are parallel and will never intersect.

Front

What is the graphical representation of the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

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 linear equation?

Back

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