To solve the system of equations:
- \( x + y = 4 \) (Equation 1)
- \( 3x + 4y = 10 \) (Equation 2)
We can use substitution or elimination. Here, we will use substitution.
From Equation 1, solve for \( y \):
\[ y = 4 - x \]
Now, substitute this expression for \( y \) into Equation 2:
\[ 3x + 4(4 - x) = 10 \]
Distribute the 4:
\[ 3x + 16 - 4x = 10 \]
Combine like terms:
\[ -1x + 16 = 10 \]
Subtract 16 from both sides:
\[ -1x = 10 - 16 \] \[ -1x = -6 \]
Divide by -1:
\[ x = 6 \]
Now substitute \( x \) back into the equation we found for \( y \):
\[ y = 4 - 6 = -2 \]
So the solution to the system of equations is:
\[ x = 6, \quad y = -2 \]
To summarize, the solution is:
\[ (x, y) = (6, -2) \]