Question

Which method will you use and why?

How will you set up the equation needed to solve?
What is the solution expressed as an ordered pair? (x, y)
Option 1: Substitution because it's the most straightforward method.
Option 2: Set up the equation as x + y = 12 and x - y = -4.
Option 3: The solution is (8, 4).

Answer 1

The most appropriate method for solving the given equations is to set them up as x + y = 12 and x - y = -4 and then solve the system of equations. Using the Substitution method, we can find the solution as (4, 8).

Step-by-step explanation:

To determine the best method for solving the given equations, we need to analyze the options provided.

1. Option 1 suggests using the Substitution method because it is the most straightforward method. This means we can solve one equation for a variable and substitute it into the other equation.
   Option 2 suggests setting up the equation as x + y = 12 and x - y = -4. This allows us to solve the system of equations using any preferred method.
   Option 3 states that the solution is (8, 4), which represents an ordered pair.

Based on the options provided, it seems like the most appropriate choice would be Option 2. We can set up the equation as x + y = 12 and x - y = -4, and then solve the system of equations using any desired method such as Substitution, Elimination, or Graphing.

Let's use the Substitution method to solve the system of equations:

1. From the second equation, we can express x in terms of y by rearranging the equation: x = y - 4.
2. Substitute this value of x in the first equation: (y - 4) + y = 12.
3. Simplify and solve for y: 2y - 4 = 12 → 2y = 16 → y = 8.
4. Substitute the value of y back into the second equation to find x: x - 8 = -4 → x = -4 + 8 → x = 4.

The solution to the system of equations is (x, y) = (4, 8).