Solve Systems of Equations 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 does it indicate if two lines on a graph are parallel?

Back

The system has no solution because the lines never intersect.

Front

What does it indicate if two lines on a graph coincide?

Back

The system has infinite solutions because the lines are the same.

Front

How do you find the solution to the system y = 2x + 1 and y = 4x - 1 by graphing?

Back

Graph both equations and identify the intersection point, which is (1, 3).

Front

What is the slope of the line represented by the equation y = mx + b?

Back

The slope (m) indicates the steepness and direction of the line.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What is the graphical representation of the equation y = 3?

Back

A horizontal line that crosses the y-axis at (0, 3).