Final answer:
The system of equations is solved by eliminating variable y, giving us x = -4. Upon substituting x in the second equation, we find y = 0. Therefore, the solution is (x, y) = (-4, 0), which is not presented in the given options.
Step-by-step explanation:
To solve the system of equations using linear combination and eliminate the variable y, we need to manipulate the equations so that when they are added, the y terms cancel out. The equations given are:
- Equation 1: 2x - 9y = -8
- Equation 2: 5x + y = -20
To eliminate y, we can multiply Equation 2 by 9 to make the coefficient of y in both equations the same with opposite signs.
- Modified Equation 2: 45x + 9y = -180
Now, add Equation 1 and the Modified Equation 2:
2x - 9y + 45x + 9y = -8 + (-180)
Combining like terms, we get: 47x = -188
Divide both sides by 47 to find the value of x: x = -4
Now, plug x = -4 back into Equation 2 to find y: 5(-4) + y = -20 -20 + y = -20
Add 20 to both sides: y = 0
Therefore, the solution to the system of equations is (x, y) = (-4, 0), which is not listed in the given options. It looks like the options provided do not match the correct solution for this particular system of equations.