Question

4а+3b=5 3а+4b=10 решение системных уравнений

Answer 1

1) Нужно поменять числа местами:

4а+3b=5

4а+3b=10

2) Умножим первое уравнение на -1

-4а-3b=-5

4а+3b=10

3) Складываем

0=5

Ответ: Данная система уравнений не имеет решения

Answer 2

To solve the system of equations, we can use either the substitution method, elimination method, or matrix algebra. Let's use the elimination method to find the values of 'a' and 'b'.

Given system of equations:

1. 4a + 3b = 5
2. 3a + 4b = 10

Step 1: Multiply both sides of equation (1) by 4, and equation (2) by 3 to make the coefficients of 'a' in both equations the same.

4 * (4a + 3b) = 4 * 5 3 * (3a + 4b) = 3 * 10

This simplifies to:

1. 16a + 12b = 20
2. 9a + 12b = 30

Step 2: Now subtract equation (2) from equation (1) to eliminate 'b' and find the value of 'a':

(16a + 12b) - (9a + 12b) = 20 - 30 7a = -10

Step 3: Divide both sides by 7 to solve for 'a':

a = -10 / 7

Step 4: Substitute the value of 'a' back into one of the original equations to find 'b'. Let's use equation (1):

4a + 3b = 5 4(-10/7) + 3b = 5 -40/7 + 3b = 5

Step 5: Now, solve for 'b':

3b = 5 + 40/7 3b = (35 + 40) / 7 3b = 75 / 7

Step 6: Finally, divide by 3 to get the value of 'b':

b = (75 / 7) / 3 b = 75 / (7 * 3) b = 75 / 21 b ≈ 3.571

So, the solution to the system of equations is approximately: a ≈ -10/7 b ≈ 3.571