Final answer:
To solve the system of equations using elimination, subtract the second equation from the first to eliminate the 'f' variable. Then, substitute the value of g into one of the equations to solve for f.
Step-by-step explanation:
To solve the system of equations using elimination, we want to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate the 'f' variable by subtracting the second equation from the first. Subtracting the second equation from the first gives us: 11f + 14g - (11f + 10g) = 13 - 25. Simplifying, we get: 4g = -12. Dividing both sides of the equation by 4, we find that g = -3.
Next, we can substitute the value of g into one of the original equations to find the value of f. Substituting g = -3 into the first equation gives us: 11f + 14(-3) = 13. Simplifying, we get: 11f - 42 = 13. Adding 42 to both sides of the equation, we get: 11f = 55. Dividing both sides of the equation by 11, we find that f = 5.
Therefore, the solution to the system of equations is f = 5 and g = -3.