4.2 Introduction to 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 if a system of linear equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are exactly the same, overlapping each other.

Front

How can you determine the number of solutions in a system of linear equations?

Back

By observing the graphs of the equations: intersecting lines (one solution), parallel lines (no solution), or identical lines (infinitely many solutions).

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the y-intercept of a linear equation?

Back

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

Front

What is the slope of a linear equation?

Back

The rate of change of y with respect to x, represented as 'm' in the equation y = mx + b.

Front

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

Back

They are parallel lines and have no solutions.

Front

Back

No solution, as the lines are parallel.