Final answer:
The system of equations is solved using the addition method, leading to the solution x = -5/3 and y = -5/3.
Step-by-step explanation:
To solve the system of equations by the addition method, we have to manipulate the equations to eliminate one of the variables.
The equations given are -4x = 2y + 10 and 8x - 9y = 5.
First, we rearrange the first equation to make it easier to add to the second equation: divide the entire first equation by -2 to get 2x = -y - 5.
Next, add this new form of the first equation to the second equation so that the x terms will cancel out: 2x + 8x - y - 9y = -5 + 5.
After performing the addition, we get: 10x -10y = 0, which simplifies to x - y = 0 or x = y.
Substitute x = y into one of the original equations to find the value of x: -4x = 2x + 10 converts to -6x = 10, so x = -10/6 or -5/3.
Now that we have the value of x, we can find y by using the equation x = y, so y = -5/3.
The solution to the system of equations is x = -5/3 and y = -5/3.