System of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved simultaneously.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, resulting in no solutions for the system.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at a single point.

Front

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

Back

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

Front

How can you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will have the same slope but different y-intercepts.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, which can be either one solution (intersecting lines) or infinitely many solutions (coincident lines).

Front

What is the difference between a consistent and inconsistent system of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

How can you identify a system of equations with infinitely many solutions?

Back

If the equations represent the same line, they will have the same slope and y-intercept.