Questions: Solve the system by elimination method. x+Ay=-1 x+By=1 Where A and B are non-zero numbers with A ≠ B. Write the answer in terms of A, B. Select one: A. x=2/(-A+B), y=(-A-B)/(-A+B) B. x=(-A-B)/(-A+B), y=2/(-A+B) C. x=(-A+B)/(-A-B), y=2/(-A+B) D. x=(-A+B)/2, y=(-A+B)/(-A-B)

Solution Steps

To solve the system of equations by the elimination method, we can subtract the second equation from the first to eliminate $x$. This will allow us to solve for $y$. Once we have $y$, we can substitute it back into one of the original equations to solve for $x$.

1. Subtract the second equation from the first to eliminate $x$.
2. Solve the resulting equation for $y$.
3. Substitute $y$ back into one of the original equations to solve for $x$.

We start with the given system of equations: $$\left\{\begin{array}{l} x + A y = -1 \\ x + B y = 1 \end{array}\right.$$

To eliminate $x$, we subtract the second equation from the first: $$(x + A y) - (x + B y) = -1 - 1$$ $$x + A y - x - B y = -2$$ $$(A - B) y = -2$$

We solve for $y$ by dividing both sides by $A - B$: $$y = \frac{-2}{A - B}$$

We substitute $y = \frac{-2}{A - B}$ into the first equation $x + A y = -1$: $$x + A \left(\frac{-2}{A - B}\right) = -1$$ $$x - \frac{2A}{A - B} = -1$$

We solve for $x$ by isolating $x$: $$x = -1 + \frac{2A}{A - B}$$ $$x = \frac{-A + 2A}{A - B}$$ $$x = \frac{A}{A - B}$$

Final Answer