Systems of Equations - Graphing (Billings)

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 one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The solution is the point where the graphs of the equations intersect.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point (0, 3) on the graph.

Front

What is the slope of the line represented by the equation y = -1/2x + 4?

Back

The slope is -1/2.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, it is a solution.