Question

{3x+y=2/{5x-3y=8 решите систему уравнений Посмотреть ответы irinaorlova2 irinaorlova2 у=2-3х 5х-3(2-3х)=8 5х-6+9х=8 14х=8+6 14х=14 х=1 у=2-3*1=2-3=-1 проверка: 3*1+(-1)=2                     5*1-3(-1)=8 2\3-1=2                          5+3=8       2=2                                8=8                       olgamartynova82 olgamartynova82 3х+у=2 у=2-3х подставляем во второе уравнение 5х-3*(2-3х)=8 5х-6+9х=8  14х=14  х=1, у =2-3*1=-1

Answer 1

You have correctly solved the system of equations:

1. Start with the given equations: 3x + y = 2 ...........(1) 5x - 3y = 8 ..........(2)

2. Isolate y in equation (1): y = 2 - 3x ...........(3)

3. Substitute the value of y from equation (3) into equation (2): 5x - 3(2 - 3x) = 8

4. Simplify and solve for x: 5x - 6 + 9x = 8 14x = 8 + 6 14x = 14 x = 1

5. Now, find the value of y using the value of x in equation (3): y = 2 - 3(1) y = 2 - 3 y = -1

So, the solution to the system of equations is x = 1 and y = -1.

You also performed the verification step correctly, which confirms that the values of x and y satisfy both equations:

1. For x = 1, y = -1: 3(1) + (-1) = 2 ➔ 3 - 1 = 2 ➔ 2 = 2 (True)

2. For x = 1, y = -1: 5(1) - 3(-1) = 8 ➔ 5 + 3 = 8 ➔ 8 = 8 (True)

The solution is valid and correct. Well done!