Solve Systems by 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 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

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.

Front

How do you find the slope of a line from an equation?

Back

The slope is the coefficient of x in the equation y = mx + b.

Front

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

Back

They have the same slope and will never intersect, indicating no solution.

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other, indicating infinitely many solutions.

Front

How can you determine the y-intercept from an equation?

Back

The y-intercept is the value of y when x = 0, found in the equation y = mx + b.

Front

What is the first step in solving a system of equations by graphing?

Back

Graph each equation on the same coordinate plane.

Front

What is the significance of the intersection point of two lines?

Back

It represents the solution to the system of equations.