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The equations in this system were added to solve for y. What is the value of y?

x + 6 y = 10. Minus x + 3 y = negative 15. Equals 9 y = negative 5.
y = Negative StartFraction 9 Over 5 EndFraction
y = Negative StartFraction 5 Over 9 EndFraction
y = StartFraction 5 Over 9 EndFraction
y = StartFraction 9 Over 5 EndFraction

1 answer

To solve for \( y \) in the given system of equations, we start with the two equations:

  1. \( x + 6y = 10 \) (Equation 1)
  2. \( -x + 3y = -15 \) (Equation 2)

We can add these two equations together to eliminate \( x \):

\[ (x + 6y) + (-x + 3y) = 10 + (-15) \]

This simplifies to:

\[ (0) + (6y + 3y) = -5 \]

Which further simplifies to:

\[ 9y = -5 \]

Now, we can solve for \( y \):

\[ y = -\frac{5}{9} \]

Thus, the value of \( y \) is:

\[ \boxed{-\frac{5}{9}} \]