`{:(x = 2 y - 1),(y = 5 - 3x):}`

Answer

To solve the given system of equations:

1. **Equations Given:**
\[ x = 2y - 1 \quad \text{(Equation 1)} \]
\[ y = 5 - 3x \quad \text{(Equation 2)} \]

2. **Substituting Equation 1 into Equation 2:**
We will substitute the expression for \(x\) from Equation 1 into Equation 2.
\[ y = 5 - 3(2y - 1) \]

3. **Expanding the Equation:**
Now, we expand the right-hand side:
\[ y = 5 - 6y + 3 \]

4. **Combining Like Terms:**
Combine the constant terms on the right-hand side:
\[ y = 8 - 6y \]

5. **Rearranging the Equation:**
Bring all terms involving \(y\) to one side:
\[ y + 6y = 8 \]
\[ 7y = 8 \]

6. **Solving for \(y\):**
Divide both sides by 7:
\[ y = \frac{8}{7} \]

7. **Substituting \(y\) back to find \(x\):**
Now substitute \(y\) back into Equation 1 to find \(x\):
\[ x = 2\left(\frac{8}{7}\right) - 1 \]
\[ x = \frac{16}{7} - 1 \]

8. **Finding a Common Denominator:**
Rewrite 1 as \(\frac{7}{7}\):
\[ x = \frac{16}{7} - \frac{7}{7} \]
\[ x = \frac{16 - 7}{7} \]
\[ x = \frac{9}{7} \]

9. **Final Solution:**
The solution to the system of equations is:
\[ x = \frac{9}{7}, \quad y = \frac{8}{7} \]

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