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 if a system of equations has infinitely many solutions?

Back

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

Front

How do you solve a system of equations by graphing?

Back

You graph each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Parallel lines have the same slope but different y-intercepts, meaning they never intersect and have no solutions.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, where both equations are satisfied.

Front

How can you determine the slope of a line from its equation?

Back

In the slope-intercept form (y = mx + b), the slope is the coefficient of x.

Front

What is the graphical representation of the equation y = -x + 3?

Back

It is a straight line with a slope of -1 and a y-intercept at (0, 3).

Front

What does it mean if two lines intersect at a single point?

Back

It means the system of equations has a unique solution, which is the coordinates of the intersection point.

Front

How do you find the y-intercept of a line given its equation?

Back

Set x = 0 in the equation and solve for y.