Solve the system of equations: 5x - 2y = -16 8x - 7y = 1

System of Equations:

• Equation 1: \( 5x - 2y = -16 \)
• Equation 2: \( 8x - 7y = 1 \)

Step-by-step solution:

1. Step 1: Multiply Equation 1 by 7 and Equation 2 by 2
   To eliminate y, multiply the first equation by 7 and the second equation by 2:
   Equation 1 multiplied by 7: \( 7(5x - 2y) = 7(-16) \) which results in \( 35x - 14y = -112 \).
   Equation 2 multiplied by 2: \( 2(8x - 7y) = 2(1) \) which results in \( 16x - 14y = 2 \).
2. Step 2: Subtract the modified Equation 2 from the modified Equation 1
   Subtract the second modified equation from the first modified equation:
   \( (35x - 14y) - (16x - 14y) = -112 - 2 \)
   \( 35x - 14y - 16x + 14y = -114 \)
   \( 19x = -114 \)
3. Step 3: Solve for x
   Divide by 19: \( x = -114 / 19 \)
   \( x = -6 \)
4. Step 4: Substitute x back into Equation 1 to find y
   Substitute \( x = -6 \) into the original Equation 1: \( 5x - 2y = -16 \)
   \( 5(-6) - 2y = -16 \)
   \( -30 - 2y = -16 \)
5. Step 5: Solve for y
   Add 30 to both sides: \( -2y = -16 + 30 \)
   \( -2y = 14 \)
   Divide by -2: \( y = -7 \)

Answer: x = -6, y = -7