Final answer:
To solve the system of equations using the elimination method, we can multiply one or both equations by constants to eliminate a variable. Once we have a new equation with only one variable, we can solve it and substitute the value back into one of the original equations.
Step-by-step explanation:
To solve the system of equations -1/3x - 1/6y = -1 and -2/3x + 1/6y = 3 using the elimination method, we need to eliminate one of the variables by multiplying one or both equations by a constant. In this case, we can multiply the first equation by 2 to eliminate y or the second equation by 3 to eliminate x.
If we multiply the second equation by 3, we get -2x + 1/2y = 9. Now we can add this new equation to the first equation, which gives us: -1/3x - 1/6y + (-2x + 1/2y) = -1 + 9. Simplifying, we get -7/3x + 1/3y = 8.
Now we have a new equation with only one variable, x. We can solve for x by multiplying the equation by -3 to eliminate the fraction, resulting in: 7x - y = -24. Finally, we can solve this equation together with one of the original equations to find the values of x and y.