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)

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)
Transcript text: Solve the system by elimination method. \[ \left\{\begin{array}{l} x+A y=-1 \\ x+B y=1 \end{array}\right. \] Where $A$ and $B$ are non-zero numbers with $A \neq B$. Write the answer in terms of $A, B$. Select one: A. $x=\frac{2}{-A+B}, \quad y=\frac{-A-B}{-A+B}$ B. $x=\frac{-A-B}{-A+B}, \quad y=\frac{2}{-A+B}$ C. $x=\frac{-A+B}{-A-B}, \quad y=\frac{2}{-A+B}$ D. $x=\frac{-A+B}{2}, \quad y=\frac{-A+B}{-A-B}$
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Solution

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Solution Steps

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

Solution Approach
  1. Subtract the second equation from the first to eliminate xx.
  2. Solve the resulting equation for yy.
  3. Substitute yy back into one of the original equations to solve for xx.
Step 1: Write down the system of equations

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

Step 2: Subtract the second equation from the first

To eliminate xx, we subtract the second equation from the first: (x+Ay)(x+By)=11 (x + A y) - (x + B y) = -1 - 1 x+AyxBy=2 x + A y - x - B y = -2 (AB)y=2 (A - B) y = -2

Step 3: Solve for yy

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

Step 4: Substitute yy back into one of the original equations

We substitute y=2ABy = \frac{-2}{A - B} into the first equation x+Ay=1x + A y = -1: x+A(2AB)=1 x + A \left(\frac{-2}{A - B}\right) = -1 x2AAB=1 x - \frac{2A}{A - B} = -1

Step 5: Solve for xx

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

Final Answer

The solution to the system of equations in terms of AA and BB is: x=AAB,y=2AB x = \frac{A}{A - B}, \quad y = \frac{-2}{A - B}

Comparing this with the given options, we see that the correct answer is: A. x=2A+B,y=ABA+B \boxed{\text{A. } x = \frac{2}{-A + B}, \quad y = \frac{-A - B}{-A + B}}

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