Solve the system of equations: 4x - 3y = -11 10x + 5y = 35

System of Equations:

• Equation 1: \( 4x - 3y = -11 \)
• Equation 2: \( 10x + 5y = 35 \)

Step-by-step solution:

1. Step 1: Simplify Equation 2
   Divide Equation 2 by 5 to simplify it: \( (10x + 5y) / 5 = 35 / 5 \) which gives \( 2x + y = 7 \).
2. Step 2: Express y in terms of x from the simplified Equation 2
   From \( 2x + y = 7 \), we get \( y = 7 - 2x \).
3. Step 3: Substitute y into Equation 1
   Substitute \( y = 7 - 2x \) into the first equation \( 4x - 3y = -11 \):
   \( 4x - 3(7 - 2x) = -11 \)
   \( 4x - 21 + 6x = -11 \)
4. Step 4: Solve for x
   Combine like terms: \( 10x - 21 = -11 \)
   Add 21 to both sides: \( 10x = -11 + 21 \)
   \( 10x = 10 \)
   Divide by 10: \( x = 1 \)
5. Step 5: Substitute x back to find y
   Substitute \( x = 1 \) into the equation \( y = 7 - 2x \):
   \( y = 7 - 2(1) \)
   \( y = 7 - 2 \)
   \( y = 5 \)

Answer: x = 1, y = 5