Final answer:
The best method to solve the equations y=-9 and y=-3x+3 is elimination. By setting the equations equal to each other, solving for x, and then back-substituting, the solution is found to be x = 4 and y = -9.
Step-by-step explanation:
The student has asked which pairs of equations would be best solved by elimination with the equations: y=-9 and y=-3x+3. The method of elimination is best used when you can easily cancel out one variable to solve for the other. In this case, you can add the two equations together to eliminate the y variable, since they have the same coefficient but opposite signs.
To solve these equations using elimination, you would set them equal to each other since they both equal y:
-9 = -3x + 3
Now solve for x:
3x = 3 + 9
3x = 12
x = 4
Now you can substitute x back into either original equation to find the value of y:
y = -3(4) + 3
y = -12 + 3
y = -9
We already knew y was -9 from the first equation, so this confirms our solution is correct. The solution to the system of equations is x = 4 and y = -9.