The Solution for the given system of equations is (-2) and [tex](\frac{5}{3})[/tex].
The given are linear equations as follow:
y = [tex]\frac{2}{3}x[/tex] + 3 .. ... ...(1)
and x = -2. .. .... ...(2)
We already know the first part of the solution (x) which is -2. We can find the other part (y) by putting the value of equation (2) in equation (1).
By putting the values of x in equation (1), we get
y = [tex](\frac{2}{3})(-2)[/tex] + 3
y = [tex]\frac{-4}{3}[/tex] + 3
Taking the L. C. M of denominators which will be '3', we get:
y = [tex]\frac{-4 + 9}{3}[/tex]
y = [tex]\frac{5}{3}[/tex]
So the second part (y) of the solution of the given equation is [tex]\frac{5}{3}[/tex].
Hence, the overall solution to the given system of equation is [tex](-2, \frac{5}{3})[/tex].
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