Question

Выразите переменную b через переменную a в выражении 3a + 5B = 1 2b - 4a =75a - 8b =14

Answer 1

Ответ:   b = (1 - 3a) : 5;     b = 3,5 + 2a;     b = 0,625a - 1,75/

Пошаговое объяснение:

3а + 5b = 1

5b = 1 - 3a

b = (1 - 3a) : 5;

2b - 4a = 7

2b = 7 + 4a

b = (7 + 4a) : 2

b = 7 : 2 + 4a : 2

b = 3,5 + 2a;

5a - 8b = 14

-8b = 14 - 5a

b = (14 - 5a) : (-8)

b = 14 : (-8) - 5a : (-8)

b = -1,75 + 0,625a

b = 0,625a - 1,75

Answer 2

To express variable b in terms of variable a in the given system of equations, we need to solve the system of equations. Let's go through the steps to find the value of b in terms of a:

Given system of equations:

1. 3a + 5b = 1
2. 2b - 4a = 75
3. 8b - 75a = 14

Step 1: Let's eliminate one variable from the first two equations. We'll eliminate b from equations 1 and 2:

Multiply equation 1 by 2 to make the coefficients of b in both equations the same:

2 * (3a + 5b) = 2 * 1 6a + 10b = 2

Now, equation 2 is: 2b - 4a = 75.

Step 2: To eliminate b, we can subtract the equations:

(6a + 10b) - (2b - 4a) = 2 - 75

Simplify the equation:

6a + 10b - 2b + 4a = -73 10a + 8b = -73

Step 3: Now, let's eliminate b from equations 2 and 3:

Multiply equation 2 by 4 and equation 3 by 2 to make the coefficients of b in both equations the same:

4 * (2b - 4a) = 4 * 75 8b - 16a = 300

2 * (8b - 75a) = 2 * 14 16b - 150a = 28

Step 4: Subtract the equations to eliminate b:

(8b - 16a) - (16b - 150a) = 300 - 28

Simplify the equation:

8b - 16a - 16b + 150a = 272 -8b + 134a = 272

Step 5: Now, we have two equations:

1. 10a + 8b = -73
2. -8b + 134a = 272

Step 6: We can now solve for b in terms of a using these two equations:

From equation 1, we can isolate b:

8b = -73 - 10a b = (-73 - 10a) / 8

Now, we can substitute the value of b from equation 1 into equation 2:

-8((-73 - 10a) / 8) + 134a = 272

Simplify the equation:

-73 - 10a + 134a = 272

Combine the 'a' terms:

124a - 73 = 272

Add 73 to both sides:

124a = 345

Finally, isolate 'a' by dividing both sides by 124:

a = 345 / 124

Now that we have the value of 'a', we can find the value of 'b' using the equation we derived earlier:

b = (-73 - 10 * (345 / 124)) / 8

Calculate the value of 'b':

b ≈ -5.483870968

So, the value of b in terms of a is approximately -5.483870968.