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 for a system to have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

How do you find the slope from two points?

Back

Use the formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis (x=0).

Front

How can you determine if a system has infinitely many solutions?

Back

If the equations represent the same line, they have infinitely many solutions.

Front

What is the slope of a line that rises 4 units for every 1 unit it runs?

Back

The slope is 4.

Front

What does it mean for two lines to intersect?

Back

It means they have a common solution, which is the point of intersection.

Front

How do you graph a linear equation?

Back

Find the y-intercept, plot it, then use the slope to find another point.

Front

What is the significance of the coordinates (1, -1) in a system of equations?

Back

It is the solution to the system, indicating where the lines intersect.