To solve the system of equations using the substitution method, follow these steps:
1. Write down the given system of equations:
[tex]\[
\begin{cases}
y = 2x - 5 & (1) \\
6x + 7 = y & (2)
\end{cases}
\][/tex]
2. Substitute the expression for [tex]\(y\)[/tex] from equation (1) into equation (2):
[tex]\[
6x + 7 = 2x - 5
\][/tex]
3. Rearrange and combine like terms to isolate [tex]\(x\)[/tex]:
[tex]\[
6x - 2x = -5 - 7
\][/tex]
Simplifying this:
[tex]\[
4x = -12
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-12}{4} = -3
\][/tex]
5. Substitute the value of [tex]\(x = -3\)[/tex] back into equation (1) to solve for [tex]\(y\)[/tex]:
[tex]\[
y = 2(-3) - 5
\][/tex]
Simplify the right-hand side:
[tex]\[
y = -6 - 5 = -11
\][/tex]
6. Write down the solution for the system of equations:
[tex]\[
(x, y) = (-3, -11)
\][/tex]
Hence, the solution to the system of equations is [tex]\(\boxed{(-3, -11)}\)[/tex].
