Answer:
The best method to use for solving the given system of equations depends on personal preference and the specific context. However, typically, the elimination method (option B) is a good choice when you have a system of linear equations like this one. Here's why:
1. Elimination Method: In this method, you can manipulate the equations by adding or subtracting them to eliminate one of the variables. In your case, you can easily eliminate the variable y by adding the two equations together or subtracting one from the other.
4x + y = 1
2x - y = 8
If you add the two equations together, the y terms will cancel out:
(4x + y) + (2x - y) = 1 + 8
6x = 9
Now, you can solve for x:
6x = 9
x = 9/6
x = 3/2
Once you've found the value of x, you can substitute it back into one of the original equations to solve for y.
4x + y = 1
4(3/2) + y = 1
6 + y = 1
Subtract 6 from both sides:
y = 1 - 6
y = -5
So, the solution to the system is x = 3/2 and y = -5.
The elimination method is straightforward and often the most efficient way to solve systems of linear equations. However, other methods like the substitution method (option A) or graphing (option C) can also be used effectively depending on the circumstances and personal preference. The matrix method (option D) is typically used for larger systems of equations and is not necessary for this simple two-equation system.
Explanation: