Question

use elimination to solve the system of equations.
$-x + y = 1$
$x + y = 11$
$($\boxed{}$ , $\boxed{}$$)$

Explanation:

Step1: Add the two equations

To eliminate \( x \), we add the equations \(-x + y = 1\) and \(x + y = 11\) together.
\[

$$\begin{align*} (-x + y)+(x + y)&=1 + 11\\ -x + y+x + y&=12\\ 2y&=12 \end{align*}$$

\]

Step2: Solve for \( y \)

Divide both sides of \( 2y = 12 \) by 2.
\[
y=\frac{12}{2}=6
\]

Step3: Substitute \( y = 6 \) into one of the original equations

We substitute \( y = 6 \) into the equation \(x + y = 11\).
\[
x+6 = 11
\]

Step4: Solve for \( x \)

Subtract 6 from both sides of \(x + 6 = 11\).
\[
x=11 - 6=5
\]

Answer:

\( (5, 6) \)