Systems of Equations - Graphing Practice

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

Back

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

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

How do you identify the solution from a graph?

Back

Look for the point where the lines intersect; that point's coordinates are the solution.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope is -3.

Front

How can you determine if two lines are parallel from their equations?

Back

If they have the same slope but different y-intercepts.

Front

What is the y-intercept of the equation 2x + 3y = 6?

Back

The y-intercept is 2 (when x = 0, y = 2).