Final answer:
To solve the given system of equations using elimination, add them to cancel out one variable, solving for the other, then back-substitute to find the second variable. The solution for the system is x = -6 and y = -6, which should be checked for correctness.
Step-by-step explanation:
To solve the system of equations using the elimination method, you can add or subtract the equations to eliminate one variable. Starting with the following two equations:
- 7x - 6y = -6
- -9x + 6y = 18
These equations are already arranged for elimination, as the coefficients of y are opposites. We can add the two equations together to eliminate the y variable:
7x - 6y + (-9x + 6y) = -6 + 18
This simplifies to:
-2x = 12
Now, divide both sides by -2 to solve for x:
x = -6
Next, we substitute x back into one of the original equations to solve for y. We'll use the first equation:
7(-6) - 6y = -6
-42 - 6y = -6
Add 42 to both sides:
-6y = 36
Finally, divide both sides by -6:
y = -6
We have now determined that x = -6 and y = -6 is the solution to the system of equations.
Remember to always check your solution by substituting the values of x and y back into the original equations to ensure they hold true.