Question

Решите систему уравнений: {a - 3b +2 = 0,2a - 4b+ 1 = 0. В ответ запишите сумму полученной пары чисел.​ Смотреть ответ iosiffinikov iosiffinikov Ответ: 4 Объяснение: Первое уравнение перепишем так 2а-6b=-4 и вычтем из него уравнение 2а-4b=-1 Получим -2b=-3 2b=3 b=1,5 2а=5 а=2,5 Сумма 2,5+1,5=4

Answer 1

Solution to the System of Equations

To solve the system of equations:

a - 3b + 2 = 0
2a - 4b + 1 = 0

We can use the method of substitution or elimination. Let's use the method of elimination.

First, let's multiply the second equation by 2 to make the coefficients of `a` the same:

2(2a - 4b + 1) = 0
4a - 8b + 2 = 0

Now, we can subtract the first equation from the second equation:

(4a - 8b + 2) - (a - 3b + 2) = 0
4a - 8b + 2 - a + 3b - 2 = 0
3a - 5b = 0

Simplifying further, we have:

3a - 5b = 0
3a = 5b
a = (5/3)b

Now, we can substitute the value of `a` into the first equation:

(5/3)b - 3b + 2 = 0
(5/3)b - 9b/3 + 2 = 0
(5 - 9b + 6)/3 = 0
(11 - 9b)/3 = 0
11 - 9b = 0
9b = 11
b = 11/9

Substituting the value of `b` back into the equation `a = (5/3)b`, we get:

a = (5/3)(11/9)
a = 55/27

Therefore, the solution to the system of equations is `a = 55/27` and `b = 11/9`.

Sum of the Obtained Pair of Numbers

To find the sum of the obtained pair of numbers, we add `a` and `b`:

a + b = (55/27) + (11/9)

To simplify the sum, we need to find a common denominator:

a + b = (55/27) + (11/9)
       = (55/27) + (33/27)
       = 88/27

Therefore, the sum of the obtained pair of numbers is 88/27.

Please let me know if you need any further assistance!