3AB 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 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 is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does it mean if two lines are parallel in a system of equations?

Back

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

Front

What does it mean if two lines are coincident in a system of equations?

Back

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

Front

How do you determine the slope of a line from its equation in slope-intercept form (y = mx + b)?

Back

The slope (m) is the coefficient of x in the equation.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented by (0, b) in the equation y = mx + b.

Front

What is the first step in solving a system of equations by graphing?

Back

Graph each equation on the same coordinate plane.

Front

What does the intersection point (1, 3) represent in a system of equations?

Back

It represents the solution to the system, where x = 1 and y = 3.