Do Now Flashcard - Feb 10th: Solving Systems Graphically

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for a system of equations to have a unique solution?

Back

A unique solution occurs when the graphs of the equations intersect at exactly one point.

Front

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

Back

No solution occurs when the graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

Infinitely many solutions occur when the equations represent the same line, meaning they intersect at every point on that line.

Front

How can you determine the solution of a system of equations graphically?

Back

You can determine the solution by graphing the equations and identifying the point(s) where the graphs intersect.

Front

What is the graphical representation of the equation y = mx + b?

Back

The equation y = mx + b represents a straight line, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

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

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept can be found by setting x to 0 in the equation and solving for y.

Front

What is the significance of the point (3, 8) in the context of a system of equations?

Back

The point (3, 8) is a solution to the system, meaning it satisfies all equations in the system.

Front

What does it mean for two lines to intersect at a point?

Back

When two lines intersect at a point, it means that the coordinates of that point are the solution to the system of equations represented by those lines.