Question

X + y = 5, X - y = 9

Label variables and solve to find the two numbers

Answer 1

We are given the system of equations:

1. \( X + Y = 5 \) (Equation 1)
2. \( X - Y = 9 \) (Equation 2)

Let's solve this system step by step.

### Step 1: Solve for one of the variables

We can start by adding both equations to eliminate \(Y\):

\[
(X + Y) + (X - Y) = 5 + 9
\]

This simplifies to:

\[
2X = 14
\]

### Step 2: Solve for \(X\)

Dividing both sides by 2:

\[
X = 7
\]

### Step 3: Substitute \(X\) back into one of the original equations

Now, we can substitute \(X = 7\) back into Equation 1:

\[
7 + Y = 5
\]

### Step 4: Solve for \(Y\)

Subtracting 7 from both sides gives us:

\[
Y = 5 - 7
\]

\[
Y = -2
\]

### Conclusion

The solution is:

\[
X = 7 \quad \text{and} \quad Y = -2
\]

Thus, the two numbers are \( X = 7 \) and \( Y = -2 \).