Final answer:
To solve the given system by substitution, x was isolated from the second equation and substituted into the first, yielding y = -1. Plugging this back into the expression for x results in x = 6. Thus, the solution is x = 6, y = -1.
Step-by-step explanation:
To solve the system by substitution, we first need to isolate one variable in one of the equations and then substitute that expression into the other equation. Looking at the second equation, -6y = x, we can easily solve for x by taking the inverse of both sides, which gives us x = -6y. We now substitute this expression into the first equation where x appears, which leads us to 5(-6y) + 9y = 21.
Simplify the equation by distributing the 5 to get -30y + 9y = 21. Combining like terms, we get -21y = 21. Dividing both sides by -21 gives us y = -1. Now that we have the value of y, we can plug it back into the expression we found for x, resulting in x = -6(-1) or x = 6. Thus, the solution to the system is x = 6, y = -1.