Question

5x+4y=6 7x+6y=10 Решить систему

Answer 1

Домножим 1 уравнение на 7,а второе на 5, получим:

35x+28y=42
35x+30y=50

Вычтем из 2 уравнения первое:
2y=8
y=4

Подставим y в любое из исходных уравнений, например, в 5x+4y=6
Получим:
5x+16=6
5x=-10
x=-2

(-2;4) - решение системы

Ответ: (-2;4)

Answer 2

Решение
{5x+4y=6  умножим на (-7)
{7x+6y=10  умножим на 5

{- 35x - 28y = - 42
  {35x + 30y = 50
складываем
2y = 8
y = 4

{y = 4
 {x+4*4=6

{y = 4
{x = 6 - 16

{x = - 10
{y = 4
Ответ: (- 10; 4)

Answer 3

To solve the system of equations:

1. 5x + 4y = 6
2. 7x + 6y = 10

We can use either the substitution method or the elimination method. I'll use the elimination method here:

Step 1: Multiply both sides of equation 1 by 3 and equation 2 by -2 to make the coefficients of x the same:

1. 15x + 12y = 18
2. -14x - 12y = -20

Step 2: Add both equations to eliminate the y variable:

(15x + 12y) + (-14x - 12y) = 18 - 20 x = -2

Step 3: Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use equation 1:

5(-2) + 4y = 6 -10 + 4y = 6 4y = 6 + 10 4y = 16 y = 16 / 4 y = 4

So, the solution to the system of equations is x = -2 and y = 4.