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What is the solution to the system of equations?

[tex]\[
\begin{array}{l}
y=\frac{2}{3}x + 3 \\
x = -2
\end{array}
\][/tex]

A. [tex]\(\left(-2, -\frac{15}{2}\right)\)[/tex]

B. [tex]\(\left(-2, \frac{5}{3}\right)\)[/tex]

C. [tex]\(\left(-2, \frac{11}{6}\right)\)[/tex]

D. [tex]\(\left(-2, \frac{13}{3}\right)\)[/tex]


Sagot :

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]