Solve the system of equations: { 2a + 3b = 0, 7a - 2b = -25

The system of equations is:

• 2a + 3b = 0
• 7a - 2b = -25

Step-by-step solution:

1. Step 1: Multiply the first equation by 2 and the second equation by 3 to make the coefficients of 'b' have the same absolute value.
   2 * (2a + 3b) = 2 * 0 => 4a + 6b = 0
   3 * (7a - 2b) = 3 * -25 => 21a - 6b = -75
2. Step 2: Now we have:
   4a + 6b = 0
   21a - 6b = -75
3. Step 3: Add the two modified equations together to eliminate 'b'.
   (4a + 6b) + (21a - 6b) = 0 + (-75)
   4a + 6b + 21a - 6b = -75
   25a = -75
4. Step 4: Solve for 'a'.
   a = -75 / 25
   a = -3
5. Step 5: Substitute the value of 'a' (-3) back into the original first equation (2a + 3b = 0) to solve for 'b'.
   2(-3) + 3b = 0
   -6 + 3b = 0
6. Step 6: Solve for 'b'.
   3b = 6
   b = 6 / 3
   b = 2

Answer: a = -3, b = 2