Final answer:
To solve the system of equations using elimination, multiply the equations by appropriate constants to create opposites of one variable. Then, add or subtract the equations to eliminate that variable. Solve for the remaining variable and substitute it back into one of the original equations to find the value of the other variable.
Step-by-step explanation:
To solve the system of equations using elimination, we want to add or subtract the equations in order to eliminate one variable. Let's start by multiplying the first equation by -2, and the second equation by 3 to create opposites of the x terms. This gives us -8.6 - 6y = -64 and 6x - 21y = 54. Now, add the two equations together to eliminate x. -8.6 - 6y + 6x - 21y = -64 + 54. Simplify the equation to get -15y = -10. Divide both sides by -15 to solve for y, which gives y = 2/3. Substituting this value back into one of the original equations, we can solve for x. Plugging in y = 2/3 into the first equation, we get 4.3 + 3(2/3) = 32. Simplify the equation to get 4.3 + 2 = 32. Combine like terms to get 6.3 = 32. Subtract 4.3 from both sides to solve for x, which gives x = 27.7. Therefore, the solution to the system of equations is x = 27.7 and y = 2/3.