Solve the system of equations: \begin{cases} 2y = 5 - 7x, \\ y = 3 - 3x. \end{cases}

Solve the system of equations:

• \[\begin{cases} 2y = 5 - 7x, \\ y = 3 - 3x. \end{cases}\]

Пошаговое решение:

1. From the second equation, we have \( y = 3 - 3x \). Substitute this expression for \( y \) into the first equation:
2. \( 2(3 - 3x) = 5 - 7x \)
3. \( 6 - 6x = 5 - 7x \)
4. Add \( 7x \) to both sides:
5. \( 6 - 6x + 7x = 5 - 7x + 7x \)
6. \( 6 + x = 5 \)
7. Subtract 6 from both sides:
8. \( 6 + x - 6 = 5 - 6 \)
9. \( x = -1 \)
10. Now substitute \( x = -1 \) into the second equation to find \( y \):
11. \( y = 3 - 3(-1) \)
12. \( y = 3 + 3 \)
13. \( y = 6 \)

Answer: x = -1, y = 6