Solve the system of equations: 10x - 9y = 8, 21y + 15x = 0,5

Solution for system (д):

Step-by-step solution:

1. Step 1: Rearrange the equations for clarity.
   Equation 1: 15x + 21y = 0.5
   Equation 2: 10x - 9y = 8
2. Step 2: Multiply the equations to eliminate 'y'.
   Multiply Equation 1 by 1: 15x + 21y = 0.5
   Multiply Equation 2 by 2.333... (or 7/3 to be exact for cleaner math) to make the y coefficients opposites: (10x - 9y) * (7/3) = 8 * (7/3) => 70/3 x - 21y = 56/3. Alternatively, to avoid fractions, let's multiply the first equation by 1 and the second by 7/3, or multiply the first equation by 1 and the second by 7/3 and then add the equations. A simpler approach is to multiply the first equation by 3 and the second by 7 to get 63y in both:
   3 * (15x + 21y = 0.5) => 45x + 63y = 1.5
   7 * (10x - 9y = 8) => 70x - 63y = 56
3. Step 3: Add the modified equations together.
   (45x + 63y) + (70x - 63y) = 1.5 + 56
   115x = 57.5
4. Step 4: Solve for 'x'.
   x = 57.5 / 115
   x = 0.5
5. Step 5: Substitute the value of 'x' into one of the original equations to solve for 'y'.
   Using the second original equation: 10x - 9y = 8
   10(0.5) - 9y = 8
   5 - 9y = 8
6. Step 6: Solve for 'y'.
   -9y = 8 - 5
   -9y = 3
   y = 3 / -9
   y = -1/3

Answer: x = 0.5, y = -1/3