Let's solve the given system of equations step-by-step to find the solution:
The system of equations is:
[tex]\[ y = \frac{2}{3} x + 3 \][/tex]
[tex]\[ x = -2 \][/tex]
1. Begin by substituting [tex]\( x = -2 \)[/tex] into the equation for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{2}{3}(-2) + 3 \][/tex]
2. Simplify the expression:
[tex]\[ y = -\frac{4}{3} + 3 \][/tex]
3. To add [tex]\(-\frac{4}{3}\)[/tex] and [tex]\(3\)[/tex], first convert [tex]\(3\)[/tex] to a fraction with the same denominator. [tex]\(3\)[/tex] is equivalent to [tex]\(\frac{9}{3}\)[/tex]:
[tex]\[ y = -\frac{4}{3} + \frac{9}{3} \][/tex]
4. Combine the fractions:
[tex]\[ y = \frac{-4 + 9}{3} \][/tex]
[tex]\[ y = \frac{5}{3} \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ \left( -2, \frac{5}{3} \right) \][/tex]
Thus, the correct answer is:
[tex]\[ \left( -2, \frac{5}{3} \right) \][/tex]
