Question

(25х-7)-3(5-4у)= -76(7у-2)-(4+3х)=23 Виконати способом додаванням.

Answer 1

{(25x-7)-3(5-4y)=-76  {25x-7-15+12y=-76  {25x+12y= -54 | *3    { 75x+36y=-162

{(7y-2)-(4+3x)=23       {7y-2-4-3x=23           {-3x+7y=29       | *25  {-75x+175у=725 

 Теперь сложим два ур-ия, исключится х: Второе уравнение можно переписатьв старом виде ( мы как бы его снова можем теперь разделить на 25).

{211у=563   {y=563/211                   { y=563/211         {y=563/211

{-3x+7y=29  {-3x=29-7*(563/211)   {-3x=2178/211    {x=-726/211

 

 

 

 

 

 

 

 

Answer 2

I can help you solve this system of equations by the method of addition. Here are the steps:

1. Rewrite the system as follows:

$$ \begin{cases} 25x - 7 - 3(5 - 4y) = -76 \\ (7y - 2) - (4 + 3x) = 23 \end{cases} $$

2. Simplify the equations by expanding the brackets and collecting like terms:

$$ \begin{cases} 25x + 12y = -62 \\ -3x + 7y = 29 \end{cases} $$

3. Multiply the first equation by 3 and the second equation by 25 to eliminate the x-term:

$$ \begin{cases} 75x + 36y = -186 \\ -75x + 175y = 725 \end{cases} $$

4. Add the equations to get a single equation in y:

$$ 211y = 539 $$

5. Solve for y by dividing both sides by 211:

$$ y = \frac{539}{211} $$

6. Substitute the value of y into any of the original equations to find x. For example, using the first equation:

$$ 25x + 12 \left( \frac{539}{211} \right) = -62 $$

7. Simplify and solve for x by isolating x on one side:

$$ x = \frac{-62 - 12 \left( \frac{539}{211} \right)}{25} $$

8. Simplify the fractions by reducing them to lowest terms:

$$ x = \frac{-1556}{525} $$

9. The solution of the system is the ordered pair (x, y):

$$ \left( \frac{-1556}{525}, \frac{539}{211} \right) $$

You can check your answer by plugging the values of x and y into the original equations and verifying that they are true. You can also use online calculators to solve equations and systems of equations, such as [this one](https://www.kontrolnaya-rabota.ru/s/equal-one/), [this one](https://allcalc.ru/node/1825), or [this one](https://pocketteacher.ru/solve-page). I hope this helps you understand the method of addition for solving systems of equations.