Systems of Equations Graphing Do Now

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

The lines intersect at exactly one point.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into both equations; if both are true, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on the same coordinate plane.

Front

What is the solution to the system of equations: y = 2x + 1 and y = 2x - 3?

Back

No solution (the lines are parallel).

Front

What is the solution to the system of equations: y = x + 2 and y = -x + 4?

Back

(1, 3) (the lines intersect at this point).

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis.