System of Equations Graphing

Front

What does it mean if a system of linear equations has one solution?

Back

The two lines intersect at one point.

Front

What are the characteristics of parallel lines in a system of equations?

Back

Parallel lines have no solutions; they never intersect.

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The two lines are the same line.

Front

How do you graph the equation y = mx + b?

Back

Plot the y-intercept (b) and use the slope (m) to find another point.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope is 3.

Front

How do you find the solution of a system of equations by graphing?

Back

Graph both equations and identify the point of intersection.

Front

What is the y-intercept of the equation y = -2x + 5?

Back

The y-intercept is 5.

Front

What does the term 'slope' refer to in a linear equation?

Back

Slope refers to the steepness of the line, calculated as rise over run.

Front

How can you determine if a system of equations is inconsistent?

Back

If the lines are parallel, the system is inconsistent with no solutions.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

The solution is (1, 3).