To solve the given system of equations:
[tex]\[
\left\{
\begin{array}{l}
y = 6x - 11 \\
-2x - 3y = -7
\end{array}
\right.
\][/tex]
we will follow a systematic approach.
1. Substitute [tex]\( y \)[/tex] from the first equation into the second equation:
The first equation is:
[tex]\[
y = 6x - 11
\][/tex]
Substitute [tex]\( y = 6x - 11 \)[/tex] into the second equation:
[tex]\[
-2x - 3(6x - 11) = -7
\][/tex]
2. Simplify and solve for [tex]\( x \)[/tex]:
Distribute the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[
-2x - 18x + 33 = -7
\][/tex]
Combine like terms:
[tex]\[
-20x + 33 = -7
\][/tex]
Subtract 33 from both sides:
[tex]\[
-20x = -7 - 33
\][/tex]
[tex]\[
-20x = -40
\][/tex]
Divide both sides by [tex]\(-20\)[/tex]:
[tex]\[
x = \frac{-40}{-20}
\][/tex]
[tex]\[
x = 2
\][/tex]
3. Substitute [tex]\( x = 2 \)[/tex] back into the first equation to find [tex]\( y \)[/tex]:
Using the first equation:
[tex]\[
y = 6x - 11
\][/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 6(2) - 11
\][/tex]
[tex]\[
y = 12 - 11
\][/tex]
[tex]\[
y = 1
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
(x, y) = (2, 1)
\][/tex]
Among the given options, the correct solution is:
[tex]\[
(2, 1)
\][/tex]
