Question

Покажіть як розв'язати систему рівнянь способом додавання на прикладі {3y - 7x = 4, {2y+5x=22 Смотреть ответ Alisaggg Alisaggg Ответ:,...........................

Answer 1

To solve the system of equations using the method of addition, also known as the method of elimination, we need to eliminate one variable by adding or subtracting the equations. Here's how you can solve the system of equations:

Step 1: Write down the equations

The given system of equations is: ``` 3y - 7x = 4 ---(1) 2y + 5x = 22 ---(2) ```

Step 2: Multiply the equations

To eliminate one variable, we need to make the coefficients of either x or y the same in both equations. In this case, let's eliminate the variable x. Multiply equation (1) by 5 and equation (2) by 7 to make the coefficients of x the same: ``` 15y - 35x = 20 ---(3) 14y + 35x = 154 ---(4) ```

Step 3: Add the equations

Now, add equation (3) and equation (4) to eliminate the variable x: ``` 15y - 35x + 14y + 35x = 20 + 154 29y = 174 ```

Step 4: Solve for y

Simplify the equation: ``` 29y = 174 y = 174 / 29 y = 6 ```

Step 5: Substitute y back into one of the original equations

Let's substitute y = 6 into equation (1): ``` 3(6) - 7x = 4 18 - 7x = 4 ```

Step 6: Solve for x

Simplify the equation: ``` -7x = 4 - 18 -7x = -14 x = -14 / -7 x = 2 ```

Step 7: Check the solution

To check if the solution is correct, substitute the values of x and y into the second equation: ``` 2y + 5x = 22 2(6) + 5(2) = 22 12 + 10 = 22 22 = 22 ``` The equation is true, which means the solution (x = 2, y = 6) is correct.

Therefore, the solution to the given system of equations is x = 2 and y = 6.

I hope this helps! Let me know if you have any further questions.