To solve the system of equations, we have:
- \( 5x + 3y = 29 \) (Equation 1)
- \( 2x - y = 5 \) (Equation 2)
We can use the substitution or elimination method to find the values of \( x \) and \( y \).
Let's use the substitution method. First, we can solve Equation 2 for \( y \):
\[ y = 2x - 5 \]
Now, we substitute this expression for \( y \) into Equation 1:
\[ 5x + 3(2x - 5) = 29 \]
Expanding this:
\[ 5x + 6x - 15 = 29 \]
Combine like terms:
\[ 11x - 15 = 29 \]
Next, add 15 to both sides:
\[ 11x = 44 \]
Now, divide by 11:
\[ x = 4 \]
Now that we have \( x \), we can substitute it back into the expression we found for \( y \):
\[ y = 2(4) - 5 \] \[ y = 8 - 5 \] \[ y = 3 \]
So, the solution to the system of equations is the ordered pair:
\[ (4, 3) \]
To verify, we can plug \( x = 4 \) and \( y = 3 \) back into both original equations:
For Equation 1:
\[ 5(4) + 3(3) = 20 + 9 = 29 \quad \text{(True)} \]
For Equation 2:
\[ 2(4) - 3 = 8 - 3 = 5 \quad \text{(True)} \]
Both equations are satisfied, thus confirming that the solution is correct.
The final answer is:
\((4, 3)\)