Chapter 4 - Graphing Systems of Equations

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 two lines to intersect on a graph?

Back

It means that the two equations have one solution, which is the point where the lines meet.

Front

What is the solution to a system of equations when the lines are parallel?

Back

No solution, because parallel lines never intersect.

Front

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

Back

It means that the two equations represent the same line, so every point on the line is a solution.

Front

How do you find the solution to a system of equations graphically?

Back

By plotting both equations on the same graph and identifying the point(s) where they intersect.

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.

Front

What is the slope of a line?

Back

The slope is a measure of how steep a line is, calculated as the rise over run.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

If two lines have the same slope but different y-intercepts, what can be said about their solutions?

Back

They are parallel lines and have no solution.

Front

What is the point of intersection of the lines represented by the equations y = x + 2 and y = -x + 4?

Back

(2, 4) - This is the solution to the system.