To solve the given sets of simultaneous equations step-by-step, we arrive at the following values for each variable:
1. For the equations [tex]\(-7c + 3d = 26\)[/tex] and [tex]\(c + 6d = -23\)[/tex]:
[tex]\[
\begin{cases}
-7c + 3d = 26 \\
c + 6d = -23
\end{cases}
\][/tex]
Solving these, we find:
[tex]\[
c = -5, \quad d = -3
\][/tex]
2. For the equations [tex]\(-7e + 6f = 24\)[/tex] and [tex]\(3e + f = -21\)[/tex]:
[tex]\[
\begin{cases}
-7e + 6f = 24 \\
3e + f = -21
\end{cases}
\][/tex]
Solving these, we find:
[tex]\[
e = -6, \quad f = -3
\][/tex]
3. For the equations [tex]\(-7x + 5y = -7\)[/tex] and [tex]\(x + 7y = -53\)[/tex]:
[tex]\[
\begin{cases}
-7x + 5y = -7 \\
x + 7y = -53
\end{cases}
\][/tex]
Solving these, we find:
[tex]\[
x = -4, \quad y = -7
\][/tex]
4. For the equations [tex]\(5a + 2b = 21\)[/tex] and [tex]\(-3a - 5b = -5\)[/tex]:
[tex]\[
\begin{cases}
5a + 2b = 21 \\
-3a - 5b = -5
\end{cases}
\][/tex]
Solving these, we find:
[tex]\[
a = 5, \quad b = -2
\][/tex]
5. For the equations [tex]\(6v + w = -4\)[/tex] and [tex]\(-6v + 5w = 16\)[/tex]:
[tex]\[
\begin{cases}
6v + w = -4 \\
-6v + 5w = 16
\end{cases}
\][/tex]
Solving these, we find:
[tex]\[
v = -1, \quad w = 2
\][/tex]
6. For the equations [tex]\(-3g + h = -6\)[/tex] and [tex]\(6g - 5h = 21\)[/tex]:
[tex]\[
\begin{cases}
-3g + h = -6 \\
6g - 5h = 21
\end{cases}
\][/tex]
Solving these, we find:
[tex]\[
g = 1, \quad h = -3
\][/tex]
The results derived from these equations are:
[tex]\[
\begin{array}{cccc}
c = -5 & \quad & e = -6 & \quad \\
d = -3 & \quad & f = -3 & \quad \\
x = -4 & \quad & a = 5 & \quad \\
y = -7 & \quad & b = -2 & \quad \\
v = -1 & \quad & g = 1 & \quad \\
w = 2 & \quad & h = -3 & \quad
\end{array}
\][/tex]
