Solving Systems of Two Linear Equations

Front

What are coincident lines in a system of linear equations?

Back

Coincident lines are lines that lie on top of each other, representing the same equation. They have infinitely many solutions.

Front

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

Back

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

Front

What do the graphs of intersecting lines represent in a system of linear equations?

Back

Intersecting lines represent a unique solution to the system, where the two lines cross at one point.

Front

How can you identify coincident lines from equations?

Back

If two equations can be simplified to the same equation, they represent coincident lines.

Front

What is the graphical representation of parallel lines in a system of linear equations?

Back

Parallel lines never intersect and represent a system with no solutions.

Front

What is the significance of the slope in linear equations?

Back

The slope indicates the steepness of the line and the direction it travels. Lines with the same slope are either parallel or coincident.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you solve a system of linear equations graphically?

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.