Sure, let's solve the system of equations step by step.
Given the system:
[tex]\[
\left\{
\begin{array}{l}
5x + 6x = 20 \\
4x - 3y = -23
\end{array}
\right.
\][/tex]
Step 1: Simplify the first equation.
[tex]\[
5x + 6x = 11x
\][/tex]
Thus, the first equation becomes:
[tex]\[
11x = 20
\][/tex]
Step 2: Solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{20}{11}
\][/tex]
So, we have:
[tex]\[
x = 1.8181818181818181
\][/tex]
Step 3: Substitute [tex]\( x \)[/tex] into the second equation.
The second equation is:
[tex]\[
4x - 3y = -23
\][/tex]
Substitute [tex]\( x = 1.8181818181818181 \)[/tex]:
[tex]\[
4(1.8181818181818181) - 3y = -23
\][/tex]
Calculate [tex]\( 4 \times 1.8181818181818181 \)[/tex]:
[tex]\[
4 \times 1.8181818181818181 = 7.2727272727272725
\][/tex]
Thus, the equation becomes:
[tex]\[
7.2727272727272725 - 3y = -23
\][/tex]
Step 4: Solve for [tex]\( y \)[/tex].
First, isolate the [tex]\( y \)[/tex]-term:
[tex]\[
-3y = -23 - 7.2727272727272725
\][/tex]
Calculate [tex]\( -23 - 7.2727272727272725 \)[/tex]:
[tex]\[
-23 - 7.2727272727272725 = -30.27272727272727
\][/tex]
Thus:
[tex]\[
-3y = -30.27272727272727
\][/tex]
Now, divide both sides by [tex]\(-3\)[/tex]:
[tex]\[
y = \frac{-30.27272727272727}{-3}
\][/tex]
[tex]\[
y = 10.090909090909092
\][/tex]
The solution to the system of equations is:
[tex]\[
x = 1.8181818181818181
\][/tex]
[tex]\[
y = 10.090909090909092
\][/tex]
