Question

Solve the system of equations.

2.5y + 3x = 27

5x – 2.5y = 5



What equation is the result of adding the two equations?



What is the solution to the system?

Answer 1

To solve the system of equations, we first write down the two equations clearly:

1. \( 2.5y + 3x = 27 \) (Equation 1)
2. \( 5x - 2.5y = 5 \) (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 \( (x, y) = (4, 6) \).