Question

X+2y = 27,3х – у = 11;​

Answer 1

Пошаговое объяснение:

y = 3x - 11

x + 2(3x - 11) = 27

x + 6x - 22 = 27

7x = 49

x = 7

y = 3*7 - 11 = 21 - 11 = 10

Ответ: (7;10).

Answer 2

To solve this system of linear equations for the variables x and y, you can use the method of substitution or elimination. I'll demonstrate the elimination method:

1. Start with the two equations:

   • Equation 1: x + 2y = 27
   • Equation 2: 3x - y = 11

2. Multiply Equation 1 by 3 to make the coefficients of y in both equations equal:

   • 3(x + 2y) = 3(27)

   This gives us:

   • 3x + 6y = 81

3. Now, we have the system of equations:

   • Equation 3: 3x + 6y = 81
   • Equation 2: 3x - y = 11

4. Subtract Equation 2 from Equation 3 to eliminate x:

   • (3x + 6y) - (3x - y) = 81 - 11

   Simplify:

   • 3x + 6y - 3x + y = 70

5. Combine like terms:

   • 7y = 70

6. Divide both sides by 7 to solve for y:

   • y = 10

7. Now that you have the value of y, you can substitute it back into either Equation 1 or Equation 2 to find x. Using Equation 2:

   • 3x - 10 = 11

8. Add 10 to both sides:

   • 3x = 11 + 10
   • 3x = 21

9. Divide both sides by 3 to solve for x:

   • x = 7

So, the solution to the system of equations is: x = 7 y = 10