Solve the following Systems of Linear Equations by graphing. Graph the equations.
In your submitted answer, describe what the graph looks like, and what this tells you about the solution to this System of Linear Equations.
x + y = 3
6x = -6y + 18
To graph the system of linear equations:
1. x + y = 3
2. 6x = -6y + 18
We will first rewrite each equation in slope-intercept form (y = mx + b):
1. Equation 1: x + y = 3
y = -x + 3
2. Equation 2: 6x = -6y + 18
y = -x + 3
Now, we will graph these two equations on the same coordinate plane:
The first equation is a line with a y-intercept of 3 and a slope of -1.
The second equation is also a line with a y-intercept of 3 and a slope of -1.
Both equations represent the same line since they have the same slope and y-intercept. This means that the two equations are dependent and consistent, with infinitely many solutions, and the solution is the line itself.
The graph of these two linear equations will be a single line passing through the points (0,3) and (3,0) with no intersection since the equations are representing the same line.
This tells us that the system of linear equations has infinite solutions along the line represented by y = -x + 3.