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 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 in the system.

Front

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

Back

It indicates that the system has no solutions, as the lines will never intersect.

Front

What does it mean if two equations represent the same line when graphed?

Back

It means the system has infinitely many solutions, as 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 graphs of the equations: one intersection point indicates one solution, no intersection points indicate no solutions, and overlapping lines indicate infinitely many solutions.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (positive slope rises, negative slope falls).

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.