Answer :
Sure, let's solve the system of equations step by step:
Given equations:
1. \( 3x + 2y = 25 \)
2. \( 9x + 5y = 64 \)
We can solve this system using the method of elimination or substitution. Here, I'll demonstrate the substitution method:
**Step 1: Solve for one variable in terms of the other from the first equation.**
From equation (1):
\[ 3x + 2y = 25 \]
Let's solve for \( x \):
\[ 3x = 25 - 2y \]
\[ x = \frac{25 - 2y}{3} \]
**Step 2: Substitute \( x \) from step 1 into the second equation.**
Substitute \( x = \frac{25 - 2y}{3} \) into equation (2):
\[ 9\left(\frac{25 - 2y}{3}\right) + 5y = 64 \]
**Step 3: Simplify and solve for \( y \).**
Multiply through by 3 to eliminate the fraction:
\[ 9(25 - 2y) + 15y = 192 \]
\[ 225 - 18y + 15y = 192 \]
Combine like terms:
\[ 225 - 3y = 192 \]
Subtract 225 from both sides:
\[ -3y = -33 \]
Divide both sides by -3:
\[ y = 11 \]
**Step 4: Substitute \( y = 11 \) back into the equation from step 1 to find \( x \).**
Using \( y = 11 \):
\[ x = \frac{25 - 2 \cdot 11}{3} \]
\[ x = \frac{25 - 22}{3} \]
\[ x = \frac{3}{3} \]
\[ x = 1 \]
**Step 5: Verify the solution by substituting \( x = 1 \) and \( y = 11 \) into both original equations.**
For equation (1):
\[ 3(1) + 2(11) = 3 + 22 = 25 \] (True)
For equation (2):
\[ 9(1) + 5(11) = 9 + 55 = 64 \] (True)
Therefore, the solution to the system of equations is \( x = 1 \) and \( y = 11 \).
**Conclusion:**
{x = 1, \; y = 11}
Answer:
