To solve the system of equations using elimination, we can eliminate one of the variables by adding or subtracting the equations. In this case, let's eliminate the variable "x".
We have the following system of equations:
-4x - y = -11 (Equation 1)
-4x + 7y = 11 (Equation 2)
To eliminate the "x" variable, we can subtract Equation 1 from Equation 2:
(-4x + 7y) - (-4x - y) = 11 - (-11)
Simplifying, we get:
-4x + 7y + 4x + y = 11 + 11
Combining like terms, we have:
6y = 22
Now, we can solve for "y" by dividing both sides of the equation by 6:
y = 22/6
Simplifying the fraction, we get:
y = 11/3
Now that we have the value of "y", we can substitute it back into one of the original equations to solve for "x". Let's use Equation 1:
-4x - (11/3) = -11
To simplify the equation, let's multiply both sides by 3 to get rid of the fraction:
-12x - 11 = -33
Now, let's isolate "x" by adding 11 to both sides:
-12x = -33 + 11
Simplifying, we have:
-12x = -22
Finally, divide both sides by -12 to solve for "x":
x = -22 / -12
Simplifying the fraction, we get:
x = 11/6
Therefore, the solution to the system of equations is x = 11/6 and y = 11/3.