Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

Front

What does it mean for a system of equations to have infinite solutions?

Back

A system of equations has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

How do you identify the slope from a graph?

Back

The slope is identified as the ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) where b is the y-coordinate.

Front

How can you graph a system of equations?

Back

To graph a system of equations, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

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

Back

When two lines are parallel, they have the same slope but different y-intercepts, indicating that there are no solutions to the system.

Front

What is the graphical representation of a solution to a system of equations?

Back

The graphical representation of a solution is the point of intersection of the lines representing the equations.

Front

How do you find the solution to a system of equations graphically?

Back

To find the solution graphically, locate the point where the graphs of the equations intersect.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).