Final answer:
The solution to the given system of equations is x = 1.29, y = -0.14.
Step-by-step explanation:
The given system of equations can be written as:
3x + 6y = 3
4x + y = 1
x + 4y = -4
3x - 4y = 0
To find the solution, we can solve this system using elimination or substitution:
Using elimination, we can add the first equation and the third equation, and the second equation and the fourth equation, to eliminate x:
7y = -1
-3y = -3
From these equations, we can solve for y:
y = -1/7
Substituting this value of y into any one of the equations, we find:
3x + 6(-1/7) = 3
3x - 6/7 = 3
3x = 21/7 + 6/7
3x = 27/7
x = 27/7 * 1/3
x = 9/7
Therefore, the solution to the system of equations is x = 9/7, y = -1/7, which can be written as x = 1.29, y = -0.14 (rounded to two decimal places).