Answer :
To solve the system of equations:
[tex]\[ \begin{array}{l} y=\frac{2}{3} x+3 \\ x=-2 \end{array} \][/tex]
we need to find the value of [tex]\( y \)[/tex] when [tex]\( x = -2 \)[/tex]. Follow these steps:
1. Substitute [tex]\( x = -2 \)[/tex] into the first equation [tex]\( y = \frac{2}{3}x + 3 \)[/tex]:
[tex]\[ y = \frac{2}{3}(-2) + 3 \][/tex]
2. Simplify the expression:
[tex]\[ y = \frac{2 \cdot (-2)}{3} + 3 = \frac{-4}{3} + 3 \][/tex]
3. Convert [tex]\( 3 \)[/tex] to a fraction with a denominator of 3 to add to [tex]\(\frac{-4}{3}\)[/tex]:
[tex]\[ y = \frac{-4}{3} + \frac{9}{3} \][/tex]
4. Add the fractions:
[tex]\[ y = \frac{-4 + 9}{3} = \frac{5}{3} \][/tex]
So, the result is [tex]\( y = \frac{5}{3} \)[/tex].
Comparing this with the given options:
[tex]\[ \left(-2, -\frac{15}{2}\right) \left(-2, \frac{5}{3}\right) \left(-2, \frac{11}{6}\right) \left(-2, \frac{13}{3}\right) \][/tex]
The correct solution corresponds to the point [tex]\((-2, \frac{5}{3})\)[/tex].
Thus, the correct option is:
[tex]\(\boxed{2}\)[/tex]
[tex]\[ \begin{array}{l} y=\frac{2}{3} x+3 \\ x=-2 \end{array} \][/tex]
we need to find the value of [tex]\( y \)[/tex] when [tex]\( x = -2 \)[/tex]. Follow these steps:
1. Substitute [tex]\( x = -2 \)[/tex] into the first equation [tex]\( y = \frac{2}{3}x + 3 \)[/tex]:
[tex]\[ y = \frac{2}{3}(-2) + 3 \][/tex]
2. Simplify the expression:
[tex]\[ y = \frac{2 \cdot (-2)}{3} + 3 = \frac{-4}{3} + 3 \][/tex]
3. Convert [tex]\( 3 \)[/tex] to a fraction with a denominator of 3 to add to [tex]\(\frac{-4}{3}\)[/tex]:
[tex]\[ y = \frac{-4}{3} + \frac{9}{3} \][/tex]
4. Add the fractions:
[tex]\[ y = \frac{-4 + 9}{3} = \frac{5}{3} \][/tex]
So, the result is [tex]\( y = \frac{5}{3} \)[/tex].
Comparing this with the given options:
[tex]\[ \left(-2, -\frac{15}{2}\right) \left(-2, \frac{5}{3}\right) \left(-2, \frac{11}{6}\right) \left(-2, \frac{13}{3}\right) \][/tex]
The correct solution corresponds to the point [tex]\((-2, \frac{5}{3})\)[/tex].
Thus, the correct option is:
[tex]\(\boxed{2}\)[/tex]
