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

How do you determine the solution from a graph?

Back

By identifying the coordinates of the intersection point of the lines.

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 coincide in a system of equations?

Back

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

Front

What is the slope of a line?

Back

The rate of change of the y-coordinate with respect to the x-coordinate, often represented as 'm'.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented as 'b' in the slope-intercept form y = mx + b.

Front

How can you find the slope from two points (x1, y1) and (x2, y2)?

Back

Using the formula m = (y2 - y1) / (x2 - x1).