Substitution Success: Solve for x and y in x + 4y = 5 - 3y, 2x + 3y = 6

To solve the given system of equations using the substitution method, follow these steps:

• Step A: Simplify and solve the first equation for $x$.
  Given: $x + 4y = 5 - 3y$
  Combine like terms: $x + 4y + 3y = 5$$x + 7y = 5$
  Now solve for $x$: $x = 5 - 7y$

• Step B: Substitute this expression for $x$ in the second equation: $2x + 3y = 6$
  Substitute $x = 5 - 7y$: $2(5 - 7y) + 3y = 6$
  Expand and simplify: $10 - 14y + 3y = 6$$10 - 11y = 6$$-11y = 6 - 10$$-11y = -4$
  Solving for $y$: $y = \frac{-4}{-11} = \frac{4}{11}$

• Step C: Substitute $y = \frac{4}{11}$ back into the equation for $x$: $x = 5 - 7(\frac{4}{11})$$x = 5 - \frac{28}{11}$
  Convert 5 to an equivalent fraction: $x = \frac{55}{11} - \frac{28}{11}$$x = \frac{27}{11}$

The solution to the system of equations is $x = \frac{27}{11}$ and $y = \frac{4}{11}$.