Answer:
Dependent (consistent) system
Step-by-step explanation:
The given systems of linear equations, y = ⅔w - 1, and -2w + 3y = -3 are identical.
y = ⅔w - 1
The slope-intercept form of -2w + 3y = -3 is y = ⅔w - 1. In order to prove this statement, transform -2w + 3y = -3 into its slope-intercept form, y = mx + b.
To isolate y, add 2w to both sides:
-2w + 2w + 3y = 2w - 3
3y = 2w - 3
Divide both sides by 3:
[tex]\frac{3y}{3} = \frac{2w - 1}{3}[/tex]
y = ⅔w - 1 ⇒ This proves that both equations in the given system are identical.
If graphed, their lines will coincide and appear as if there is only one line. This characterizes a dependent (consistent) system with infinitely many solutions.
A dependent system has at least one solution; a dependent system is consistent if both equations in the system have the same slope and y-intercepts. They will also have infinitely many solutions because all of the possible solutions are along the same line.
Note:
The transformation of -2w + 3y = -3 into slope-intercept form does not constitute "solving" because the solutions to the given system were not provided in this post.
