Solving Systems of Equations by Graphing

Front

The solution to a system of equations is the place at which the lines ___________.

Back

intersect.

Front

What does it mean if a system of linear equations has infinite solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

These two lines intersect at _____.

Back

(4, -2)

Front

Is the following point a solution to the given system of equations? (-1,-5) for y = -x + 2 and y = 3x - 2

Back

No

Front

The solution to this system of equations is: What is the solution to the equations y = 2x + 1 and y = -x + 7?

Back

(4, 9)

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 be parallel in the context of systems of equations?

Back

They have the same slope but different y-intercepts, resulting in no solutions.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations plotted on a coordinate plane.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are satisfied, it is a solution.

Front

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

Back

It represents the values of the variables that satisfy all equations in the system.