Systems of Equations Graphically

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for two lines to intersect on a graph?

Back

It means that the lines have a common solution, which is the point where they meet.

Front

What is the graphical representation of a system of equations?

Back

It is the visual depiction of the equations on a coordinate plane, showing their relationships.

Front

What does it indicate if two lines are parallel in a system of equations?

Back

It indicates that there is no solution, as the lines will never intersect.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where the values of the variables satisfy all equations.

Front

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

Back

By analyzing the positions of the lines: intersecting lines have one solution, parallel lines have no solution, and coincident lines have infinitely many solutions.

Front

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

Back

(1, 3) is the solution, where the two lines intersect.

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 is the slope-intercept form of a linear equation?

Back

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

Front

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

Back

By solving one equation for a variable and substituting that expression into the other equation.