Answer:
D) Infinitely many solutions
Step-by-step explanation:
Given the follwowing systems of linear equations, y = x + 2, and -3x + 3y = 6:
Transforming -3x + 3y = 6 into its slope-intercept form, y = mx + b:
-3x + 3y = 6
Add 3x to both sides:
-3x + 3x + 3y = 3x + 6
3y = 3x + 6
Divide both sides by 3:
[tex]\frac{3y}{3} = \frac{3x + 6}{3}[/tex]
y = x + 2 ⇒ This is the slope-intercept form of -3x + 3y = 6. Since they are equivalent equations, then it means that their graphed lines coincide. Since any point on either lines coincide (or also exists) on the other line, then it means that the solutions to one of the equations will satisfy the other. Therefore, the given systems of linear equations have an infinitely many solutions.
