Solutions to systems of equations

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never intersect and have the same slope.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the lines represented by the equations are parallel.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point where the lines intersect, representing the values of the variables that satisfy both equations.

Front

What does the graph of a system with one solution look like?

Back

The graph of a system with one solution shows two intersecting lines.

Front

What does the graph of a system with infinitely many solutions look like?

Back

The graph of a system with infinitely many solutions shows two overlapping lines.

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 slope of a line given two points?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

What is a system of linear equations?

Back

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