Systems of Equations - Word Problems and Graphing

Front

What are systems of equations?

Back

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

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the solution of a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and do not intersect.

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 the line is a solution.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying the point(s) of intersection.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b.