Graphing Systems of Equations

Front

What is a system of equations?

Back

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

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.

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.

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.

Front

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

Back

The slope is 1/2.

Front

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

Back

The y-intercept is 9.

Front

How do you find the intersection point of two lines graphically?

Back

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

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3) is the solution.

Front

What does it mean if two lines are parallel when graphing a system of equations?

Back

It means there is no solution, as the lines never intersect.

Front

What is the significance of the point (2, 3) in the context of a system of equations?

Back

It is the solution to the system, meaning both equations are satisfied at this point.