To solve the system of equations, we first write down the two equations clearly:
- \( 2.5y + 3x = 27 \) (Equation 1)
- \( 5x - 2.5y = 5 \) (Equation 2)
Step 1: Adding the two equations
To add the two equations, we align them:
\[ 2.5y + 3x = 27 \] \[ 5x - 2.5y = 5 \]
Now, we add the left-hand side of both equations together and the right-hand side together:
\[ (2.5y - 2.5y) + (3x + 5x) = 27 + 5 \]
This simplifies to:
\[ 0 + 8x = 32 \]
So, the result of adding the two equations is:
\[ 8x = 32 \]
Step 2: Solving for \( x \)
Dividing both sides by 8 gives:
\[ x = 4 \]
Step 3: Substitute \( x \) back to find \( y \)
Now we can substitute \( x = 4 \) back into one of the original equations. Let's use Equation 1:
\[ 2.5y + 3(4) = 27 \]
Calculating this gives:
\[ 2.5y + 12 = 27 \]
Subtracting 12 from both sides:
\[ 2.5y = 15 \]
Now divide by 2.5:
\[ y = \frac{15}{2.5} = 6 \]
Conclusion
The solution to the system of equations is:
\[ (x, y) = (4, 6) \]
Summary
- The result of adding the two equations is \( 8x = 32 \).
- The solution to the system is \( (x, y) = (4, 6) \).