Question

Решите систему : {5х+6у=28, { | х | +9y=29; З. Ы. | х | - это модуль икса. Посмотреть ответы marselo2228 marselo2228 Вот так) Надеюсь, что помог) Удачи) SiRL02 SiRL02 {5x+6y=28                          {5x+6y=28                           {x+9y=29                            {-x+9y=29                         5(29-9y)+6y=28                  5(9y-29)+6y=28          145-45y+6y=28                  45y-145+6y=28  39y=117                             51y=173 y=3                                      y=3 x=29-3*9=2                         x=3 *9-29=1                (2, 3) и (1 , 3 )

Answer 1

To solve the system of equations:

1. 5x + 6y = 28
2. |x| + 9y = 29

Let's first isolate the variable x in equation 1:

5x = 28 - 6y x = (28 - 6y) / 5

Now, substitute this value of x into equation 2:

|x| + 9y = 29 |(28 - 6y) / 5| + 9y = 29

We have two cases to consider because of the absolute value:

Case 1: (28 - 6y) / 5 is positive. In this case, |(28 - 6y) / 5| = (28 - 6y) / 5. Substitute this back into equation 2:

(28 - 6y) / 5 + 9y = 29 Multiply by 5 to get rid of the fraction:

28 - 6y + 45y = 145 Combine the y terms:

39y = 117 Divide by 39 to solve for y:

y = 3

Now, find the corresponding x value using equation 1:

5x + 6(3) = 28 5x + 18 = 28 Subtract 18 from both sides:

5x = 10 Divide by 5 to solve for x:

x = 2

So one solution is x = 2 and y = 3.

Case 2: (28 - 6y) / 5 is negative. In this case, |(28 - 6y) / 5| = -(28 - 6y) / 5. Substitute this back into equation 2:

-(28 - 6y) / 5 + 9y = 29 Multiply by 5 to get rid of the fraction:

-(28 - 6y) + 45y = 145 Distribute the negative sign:

-28 + 6y + 45y = 145 Combine the y terms:

51y = 173 Divide by 51 to solve for y:

y = 173 / 51 ≈ 3.39

Now, find the corresponding x value using equation 1:

x = (28 - 6y) / 5 x = (28 - 6(173/51)) / 5 x = (28 - 1038/51) / 5 x = (28 - 20.31) / 5 x = 7.738 / 5 x ≈ 1.547

So the second solution is x ≈ 1.547 and y ≈ 3.39.

In conclusion, the system has two solutions:

1. x = 2, y = 3
2. x ≈ 1.547, y ≈ 3.39.