Контрольные задания > Solve the system of equations: \begin{cases} 3x-y=6, \\ 5x-2y=10. \end{cases}
Вопрос:

Solve the system of equations: \begin{cases} 3x-y=6, \\ 5x-2y=10. \end{cases}

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Ответ:

Let's solve this system of equations!

Краткое пояснение: We can use the substitution or elimination method to solve this system. Let's use the elimination method.

Пошаговое решение:

  1. Multiply the first equation by -2 to eliminate the y variable:
    \[-2(3x - y) = -2(6)\] \[-6x + 2y = -12\]
  2. Write the second equation as is:
    \[5x - 2y = 10\]
  3. Add the two equations to eliminate y:
    \[(-6x + 2y) + (5x - 2y) = -12 + 10\] \[-x = -2\]
  4. Solve for x:
    \[x = 2\]
  5. Substitute x = 2 into the first original equation to solve for y:
    \[3(2) - y = 6\] \[6 - y = 6\] \[y = 0\]

Ответ: x = 2, y = 0

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