Question

2) [6x - 13y + 1 = 0, 5x+10y - 20 = 0.​

Answer 1

Ответ:

..............

Пошаговое объяснение:

....,.........

Answer 2

Ответ:

(2; 1)

Пошаговое объяснение:

Система уравнений решена способом подстановки:

{6х - 13у + 1 = 0

{5х + 10у - 20 = 0

{6х - 13у = -1

{5х + 10у = 20 | : 5

{6х - 13у = -1

{х + 2у = 4

{6х - 13у = -1

{х = 4 - 2у

1)

6х - 13у = -1

6(4 - 2у) - 13у = -1

24 - 12у - 13у = -1

-12у - 13у = -1 - 24

-25у = -25

у = -25 : (-25)

у = 1

2)

х = 4 - 2у

х = 4 - 2 * 1

х = 4 - 2

х = 2

Answer 3

To solve this system of linear equations:

1. First, let's simplify both equations if needed.

Equation 1: 6x - 13y + 1 = 0 Equation 2: 5x + 10y - 20 = 0

2. You can choose to solve for one variable in one equation and then substitute it into the other equation or use the method of elimination. Let's use the elimination method in this case.

3. Multiply Equation 2 by 13 to make the coefficients of y in both equations cancel each other when added together:

Equation 1: 6x - 13y + 1 = 0 Equation 2 (multiplied by 13): 65x + 130y - 260 = 0

4. Now, add the two equations together to eliminate the y variable:

(6x - 13y + 1) + (65x + 130y - 260) = 0

Combine like terms:

6x + 65x - 13y + 130y + 1 - 260 = 0

71x + 117y - 259 = 0

5. Now, you have a single equation with one variable:

71x + 117y - 259 = 0

6. Solve for one variable. Let's solve for x:

71x = 259 - 117y

x = (259 - 117y) / 71

7. Now, substitute this expression for x back into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:

6x - 13y + 1 = 0

6((259 - 117y) / 71) - 13y + 1 = 0

Multiply both sides by 71 to clear the fraction:

6(259 - 117y) - 13y*71 + 71 = 0

Distribute and simplify:

1554 - 702y - 927y + 71 = 0

Combine like terms:

-1629y + 1625 = 0

-1629y = -1625

Now, divide by -1629 to solve for y:

y = -1625 / -1629

y ≈ 1 (rounded to three decimal places)

8. Now that you have the value of y, you can substitute it back into the expression for x that we found earlier:

x = (259 - 117y) / 71 x = (259 - 117*1) / 71 x = (259 - 117) / 71 x = 142 / 71 x = 2

So, the solution to the system of equations is x = 2 and y ≈ 1.