Контрольные задания > Solve the system of equations: 10x - 9y = 21y + 15x =
Вопрос:

Solve the system of equations: 10x - 9y = 21y + 15x =

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Ответ:

System of Equations:

  • 10x - 9y = ...
  • 21y + 15x = ...
Explanation: To solve this system of linear equations, we can use either the substitution method or the elimination method. We will rearrange the second equation to isolate one variable and then substitute it into the first equation, or manipulate both equations to eliminate one variable.

Step-by-step solution:

  1. Rearrange the equations:
    Equation 1: 10x - 9y = A
    Equation 2: 15x + 21y = B (assuming A and B are the values on the right side of the equals sign which are not fully visible in the image)
  2. Method of Elimination: Multiply the first equation by a factor and the second equation by another factor so that the coefficients of one variable are opposites. For example, to eliminate x, multiply Eq. 1 by 3 and Eq. 2 by -2:
    3 * (10x - 9y = A) => 30x - 27y = 3A
    -2 * (15x + 21y = B) => -30x - 42y = -2B
  3. Add the modified equations:
    (30x - 27y) + (-30x - 42y) = 3A - 2B
    -69y = 3A - 2B
    y = (3A - 2B) / -69
  4. Substitute y back into one of the original equations to solve for x:
    10x - 9 * ((3A - 2B) / -69) = A
    10x + 9 * ((3A - 2B) / 69) = A
    10x = A - 9 * ((3A - 2B) / 69)
    x = (A - 9 * ((3A - 2B) / 69)) / 10

Answer: The solution for x and y depends on the values A and B, which are not fully visible in the image.

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