Final answer:
After substituting “y=2x-4” into “6x-3y=12”, we find that the original system is dependent with infinitely many solutions, which are all the points on the line “y = 2x - 4”.
Step-by-step explanation:
To solve the system of equations y=2x-4 and 6x-3y=12 by substitution, first solve the first equation for y, which has already been done. Next, substitute the expression for y from the first equation into the second equation:
- Replace y in the second equation with the expression from the first equation: 6x - 3(2x-4) = 12.
- Simplify and solve for x: 6x - 6x + 12 = 12, which reduces to 12 = 12. This result means that the two equations are equivalent, so there are infinitely many solutions.
Thus, the original system is dependent, and the solution is the entire line represented by y = 2x - 4.