Final answer:
The solution to the system of equations is that there are infinitely many solutions, as the two equations are equivalent and represent the same line.
Step-by-step explanation:
The solution to the system of equations 8x+4y=12 and y=-2x+3 can be found using the substitution method. Since the second equation is already solved for y, substitute the expression for y from the second equation into the first equation.
Substitute y=-2x+3 into the first equation:
- 8x + 4(-2x+3) = 12
- 8x - 8x + 12 = 12
- 12 = 12
The x terms cancel each other out, leaving a statement 12=12, which is always true. This means the system has infinitely many solutions as the two equations are equivalent and represent the same line.