Solving Sytems of Equations (Graphing)

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 infinite solutions?

Back

It means that the equations represent the same line, and every point on the line is a solution.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

How do you find the intersection of two lines graphically?

Back

By plotting both lines on the same graph and identifying the point where they cross.

Front

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

Back

No Solution (the lines are parallel).

Front

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

Back

(1, 2) (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 of a line?

Back

The y-coordinate of the point where the line crosses the y-axis.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

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

Back

A straight line where m is the slope and b is the y-intercept.