Let's solve the system of linear equations:
[tex]\[
\begin{cases}
6x + 3y = 12 \\
4x + y = 14
\end{cases}
\][/tex]
### Step 1: Express one variable in terms of the other
First, we can solve the second equation for [tex]\( y \)[/tex]:
[tex]\[
4x + y = 14 \\
y = 14 - 4x
\][/tex]
### Step 2: Substitute [tex]\( y \)[/tex] in the other equation
Next, substitute this expression for [tex]\( y \)[/tex] in the first equation:
[tex]\[
6x + 3(14 - 4x) = 12
\][/tex]
### Step 3: Simplify and solve for [tex]\( x \)[/tex]
Simplify the equation:
[tex]\[
6x + 42 - 12x = 12 \\
-6x + 42 = 12 \\
-6x = 12 - 42 \\
-6x = -30 \\
x = 5
\][/tex]
### Step 4: Solve for [tex]\( y \)[/tex]
Now that we have [tex]\( x = 5 \)[/tex], substitute this value back into the equation [tex]\( y = 14 - 4x \)[/tex]:
[tex]\[
y = 14 - 4(5) \\
y = 14 - 20 \\
y = -6
\][/tex]
### Conclusion
The solution to the system of equations is:
[tex]\[
x = 5, \, y = -6
\][/tex]
Thus, the coordinates of the solution are [tex]\( \boxed{(5, -6)} \)[/tex].
