Question

use elimination to solve the system of equations.
$x + 4y = 11$
$x - 6y = 11$
$\left(\square, \square\
ight)$

Explanation:

Step1: Subtract the two equations

We have the system:
\[

$$\begin{cases} x + 4y = 11 \\ x - 6y = 11 \end{cases}$$

\]
Subtract the second equation from the first equation: \((x + 4y)-(x - 6y)=11 - 11\)
Simplify the left - hand side: \(x+4y - x + 6y=0\), which gives \(10y = 0\)

Step2: Solve for y

From \(10y=0\), divide both sides by 10: \(y=\frac{0}{10}=0\)

Step3: Substitute y into one of the original equations

Substitute \(y = 0\) into the first equation \(x+4y = 11\). We get \(x+4\times0=11\), which simplifies to \(x=11\)

Answer:

\((11,0)\)