Let's solve the given system of equations step-by-step. The system is:
[tex]\[
\begin{array}{l}
y = 6x \quad \text{(Equation 1)} \\
-x + 2y = -11 \quad \text{(Equation 2)}
\end{array}
\][/tex]
### Step 1: Substitute [tex]\( y \)[/tex] from Equation 1 into Equation 2
Since Equation 1 tells us that [tex]\( y = 6x \)[/tex], we can substitute [tex]\( 6x \)[/tex] for [tex]\( y \)[/tex] in Equation 2. This gives us:
[tex]\[
-x + 2(6x) = -11
\][/tex]
### Step 2: Simplify the resulting equation
Now, distribute the 2 in [tex]\( 2(6x) \)[/tex]:
[tex]\[
-x + 12x = -11
\][/tex]
Combine the like terms:
[tex]\[
11x = -11
\][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Divide both sides of the equation by 11:
[tex]\[
x = \frac{-11}{11} = -1
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( -1 \)[/tex].
### Step 4: Substitute [tex]\( x \)[/tex] back into Equation 1 to find [tex]\( y \)[/tex]
Now that we have [tex]\( x = -1 \)[/tex], substitute it back into Equation 1 to find [tex]\( y \)[/tex]:
[tex]\[
y = 6(-1) = -6
\][/tex]
So, the value of [tex]\( y \)[/tex] is [tex]\( -6 \)[/tex].
### Final Solution
Thus, the solution to the system of equations is:
[tex]\[
(x, y) = (-1, -6)
\][/tex]
