Sure, let's solve the system of equations using the substitution method step-by-step:
We are given the system of equations:
[tex]\[
\left\{\begin{array}{ll}
7x - 6y & = -100 \\
x & = -2y
\end{array}\right.
\][/tex]
1. Substitute [tex]\(x = -2y\)[/tex] in the first equation:
The first equation is [tex]\(7x - 6y = -100\)[/tex].
Substitute [tex]\(x\)[/tex] from the second equation into the first equation:
[tex]\[
7(-2y) - 6y = -100
\][/tex]
2. Simplify the first equation:
Simplify the expression:
[tex]\[
-14y - 6y = -100
\][/tex]
Combine like terms:
[tex]\[
-20y = -100
\][/tex]
3. Solve for [tex]\(y\)[/tex]:
Divide both sides of the equation by -20:
[tex]\[
y = \frac{-100}{-20} = 5
\][/tex]
4. Substitute [tex]\(y = 5\)[/tex] back into the second equation:
The second equation is [tex]\(x = -2y\)[/tex].
Substitute [tex]\(y = 5\)[/tex] into the equation:
[tex]\[
x = -2(5) = -10
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
\boxed{(-10, 5)}
\][/tex]
Where [tex]\(x = -10\)[/tex] and [tex]\(y = 5\)[/tex].
