To solve the system of equations:
[tex]\[
\begin{array}{l}
y = \frac{2}{3}x + 3 \\
x = -2
\end{array}
\][/tex]
we will substitute the given value of [tex]\( x \)[/tex] into the first equation to find [tex]\( y \)[/tex].
1. Begin with the equations:
[tex]\[
y = \frac{2}{3}x + 3
\][/tex]
[tex]\[
x = -2
\][/tex]
2. Substitute [tex]\( x = -2 \)[/tex] into the equation for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{2}{3}(-2) + 3
\][/tex]
3. Calculate the product:
[tex]\[
y = \frac{2 \cdot (-2)}{3} + 3 = \frac{-4}{3} + 3
\][/tex]
4. Convert 3 to a fraction with a denominator of 3 to combine the fractions:
[tex]\[
y = \frac{-4}{3} + \frac{9}{3}
\][/tex]
5. Combine the fractions:
[tex]\[
y = \frac{-4 + 9}{3} = \frac{5}{3}
\][/tex]
So, the value of [tex]\( y \)[/tex] when [tex]\( x = -2 \)[/tex] is [tex]\(\frac{5}{3}\)[/tex].
Therefore, the solution to the system of equations is:
[tex]\[
\left( -2, \frac{5}{3} \right)
\][/tex]
Hence, the correct answer is:
[tex]\[
\left(-2, \frac{5}{3}\right)
\][/tex]
