Question

-3b +5b -5c = +42 -5a -4b +2c = -31 -3a -5b -1c = -18 ответ в 3 числа

Answer 1

-3b+5b-5c=42

2b-5c=42

2b=42+5c

b=21+5/2c

b=21+5/2c

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Answer 2

To find the values of variables 'a,' 'b,' and 'c,' we can solve the system of equations given:

1. -3b + 5b - 5c = 42
2. -5a - 4b + 2c = -31
3. -3a - 5b - c = -18

Let's proceed with solving the equations. We can use various methods like substitution, elimination, or matrix methods, but I'll use the elimination method.

Step 1: Let's eliminate 'b' from the first and third equations by adding them.

Adding equations (1) and (3):

(-3b + 5b) + (-5c - c) = 42 + (-18) 2b - 6c = 24 Now, simplify the equation: b - 3c = 12 ...........(Equation 4)

Step 2: Next, let's eliminate 'b' from the second and third equations by adding them.

Adding equations (2) and (3):

(-5a - 4b) + (-2c - c) = -31 + (-18) -5a - 5b - 3c = -49 Now, simplify the equation: a + b + 3c = 49 ...........(Equation 5)

Step 3: Now we have two equations (Equation 4 and Equation 5) with two unknowns 'a' and 'c.' We can solve this system of equations to find the values of 'a' and 'c.'

Let's solve equations (4) and (5):

Equation 4: b - 3c = 12 Equation 5: a + b + 3c = 49

Substitute the value of 'b' from Equation 4 into Equation 5:

a + (12 + 3c) + 3c = 49 a + 12 + 3c + 3c = 49 a + 6c + 12 = 49

Now, isolate 'a':

a + 6c = 49 - 12 a + 6c = 37 a = 37 - 6c ...........(Equation 6)

Step 4: Substitute the value of 'a' from Equation 6 into Equation 4:

b - 3c = 12 (37 - 6c) - 3c = 12 37 - 6c - 3c = 12 37 - 9c = 12

Now, isolate 'c':

-9c = 12 - 37 -9c = -25 c = -25 / -9 c = 25/9

Step 5: Now that we have the value of 'c,' we can find the values of 'a' and 'b' using Equations 6 and 4, respectively:

a = 37 - 6c a = 37 - 6 * (25/9) a = 37 - 150/9 a = 37 - 16.67 a = 20.33 (approximately)

b = b - 3c b = 12 + 3 * (25/9) b = 12 + 25/3 b = 12 + 8.33 b = 20.33 (approximately)

So, the solution to the system of equations is approximately: a ≈ 20.33, b ≈ 20.33, and c ≈ 2.78.