Checking solutions to linear systems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

You can determine the number of solutions by analyzing the graphs of the equations: one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

Front

What does it mean if two lines are parallel in a linear system?

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that the system has no solution.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The graphical representation is two lines that overlap completely, meaning they are the same line.

Front

How do you check if a point is a solution to a linear equation?

Back

Substitute the x and y values of the point into the equation. If both sides of the equation are equal, the point is a solution.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

What is the standard form of a linear equation?

Back

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

Front

What is the difference between consistent and inconsistent systems?

Back

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

Front

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

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.