Sure, let's solve the given system of equations using the method of substitution step by step. The system of equations is:
[tex]\[
\begin{array}{l}
y = -6 \\
-10x + 2y = 8
\end{array}
\][/tex]
### Step-by-Step Solution:
1. Substitute [tex]\( y \)[/tex] from the first equation into the second equation:
We know from the first equation that [tex]\( y = -6 \)[/tex]. We substitute [tex]\( y = -6 \)[/tex] into the second equation:
[tex]\[-10x + 2(-6) = 8\][/tex]
2. Simplify the equation:
Now, simplify the left side of the equation:
[tex]\[-10x + 2 \cdot (-6) = -10x - 12\][/tex]
So, the equation becomes:
[tex]\[-10x - 12 = 8\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], first add 12 to both sides of the equation:
[tex]\[-10x - 12 + 12 = 8 + 12\][/tex]
This simplifies to:
[tex]\[-10x = 20\][/tex]
Next, divide both sides by -10:
[tex]\[x = \frac{20}{-10}\][/tex]
So, [tex]\( x = -2 \)[/tex].
4. State the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
We have found [tex]\( x = -2 \)[/tex] and from the first equation we were given [tex]\( y = -6 \)[/tex].
### Conclusion:
The solution to the system of equations is:
[tex]\[
x = -2, \quad y = -6
\][/tex]
Thus, the ordered pair that satisfies both equations is [tex]\((-2, -6)\)[/tex].
