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 a graph and identifying the point where they cross.

Front

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

Back

No Solution (the lines are parallel).

Front

What is the solution to the system of equations represented by the lines y = x + 1 and y = -x + 5?

Back

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

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope is represented by 'm' and indicates the steepness of the line.

Front

What does the y-intercept represent in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in y = mx + b.

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 solution to a system of equations?

Back

The point(s) where the lines intersect on a graph.