Let's go through the solution step by step based on the equations you've provided:
-
Start with the first equation:
\[ x + 3y = 7 \]
Isolate \( x \):
\[ x = 7 - 3y \] -
Substitute \( x = 7 - 3y \) into the second equation:
\[ 2x + 4y = 8 \]
\[ 2(7 - 3y) + 4y = 8 \]
\[ 14 - 6y + 4y = 8 \] -
Simplify and solve for \( y \):
\[ 14 - 2y = 8 \]
\[ -2y = 8 - 14 \]
\[ -2y = -6 \]
\[ y = 3 \] -
Substitute \( y = 3 \) back into the equation \( x = 7 - 3y \):
\[ x = 7 - 3(3) \]
\[ x = 7 - 9 \]
\[ x = -2 \] -
Finally, write the solution as an ordered pair:
\[ (-2, 3) \]
So, the solution to the system of equations is \( (-2, 3) \).