Question

A + b = 42{ 2a + 18b = 420​

Answer 1

{а + b = 42

{a + 18b = 420

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{a = 42 - b

{2 · (42 - b) + 18b = 420

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84 - 2b + 18b = 420

84 + 16b = 420

16b = 420 - 84

16b = 336

b = 336 : 16

b = 21

а = 42 - 21

а = 21

Ответ: (21; 21).

Answer 2

To solve this system of equations for the variables a and b, you can use either the substitution method or the elimination method. Here, I'll demonstrate the elimination method.

Given equations:

1. a + b = 42
2. 2a + 18b = 420

First, we can simplify equation 2 by dividing both sides by 2:

2a/2 + 18b/2 = 420/2 a + 9b = 210

Now, we have the system of equations:

1. a + b = 42
2. a + 9b = 210

We can subtract equation 1 from equation 2 to eliminate the variable 'a':

(a + 9b) - (a + b) = 210 - 42

This simplifies to:

8b = 168

Now, divide both sides by 8 to solve for 'b':

8b/8 = 168/8 b = 21

Now that we've found the value of 'b,' we can substitute it back into either equation 1 or equation 2 to solve for 'a.' Let's use equation 1:

a + 21 = 42

Subtract 21 from both sides:

a = 42 - 21 a = 21

So, the solution to the system of equations is:

a = 21 b = 21