Graphing Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean to graph a linear equation?

Back

To plot all the points that satisfy the equation on a coordinate plane.

Front

What is the solution to a system of linear equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What does it mean if two lines are parallel when graphing a system of equations?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

The system has infinite solutions because the lines are the same.

Front

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

Back

Graph each equation on the same coordinate plane and identify the intersection point.

Front

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

Back

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

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How can 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.