Graphing Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect, which represents the solution(s) to the system.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

How do you graph the equation y = mx + b?

Back

Plot the y-intercept (b) on the y-axis, then use the slope (m) to find another point by rising and running from the y-intercept.

Front

What is the slope of the line represented by the equation y = 1/2x + 2?

Back

The slope is 1/2, indicating that for every 2 units you move right, you move up 1 unit.

Front

What is the y-intercept of the equation y = -3x + 9?

Back

The y-intercept is 9, which is the point where the line crosses the y-axis.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel and never intersect, the system has no solution.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Front

Solve the system by graphing: y = 2x + 1 and y = 4x - 1. What is the solution?

Back

(1, 3)

Front

Solve the system by graphing: y = 1/2x + 2 and y = -3x + 9. What is the solution?

Back

(2, 3)