System of Equations - 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 mean if a system of equations has no solution?

Back

It means the lines representing the equations are parallel and never intersect.

Front

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

Back

It means the lines representing the equations are the same line, overlapping completely.

Front

How do you graph the equation y = mx + b?

Back

Start at the y-intercept (b) on the y-axis, then use the slope (m) to find another point.

Front

What is the slope in the equation y = 6x - 4?

Back

The slope is 6.

Front

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

Back

The y-intercept is 3.

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: parallel lines have no solution, same line has infinitely many solutions, and intersecting lines have one solution.

Front

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

Back

The solution is (1, 3).