Question

Укажите какие-нибудь три решения системы: 1) [-2х+у=3 [-6х+3у=9 2)[х+у=6 [2х+2у=12 3)[х-0,5у=5 [4х-2у=20 *ПРОШУ ПОМОЧЬ. БУДУ ОЧЕНЬ БЛАГОДАРНА ЗА РЕШЕНИЕ*

Answer 1

Думаю, что ты разберешься 

Answer 2

System of Equations

The given system of equations is as follows:

1) -2x + y = 3 2) -6x + 3y = 9 3) x + y = 6 4) 2x + 2y = 12 5) x - 0.5y = 5 6) 4x - 2y = 20

To find the solutions of this system, we can use various methods such as substitution, elimination, or matrix methods. Let's solve this system using the substitution method.

Substitution Method

In the substitution method, we solve one equation for one variable and substitute it into the other equation. Let's solve equations 1) and 3) for x and y, respectively.

From equation 1), we can express y in terms of x: -2x + y = 3 y = 2x + 3

Now, substitute this value of y into equation 3): x + (2x + 3) = 6 3x + 3 = 6 3x = 3 x = 1

Substitute the value of x back into equation 1) to find y: -2(1) + y = 3 -2 + y = 3 y = 3 + 2 y = 5

Therefore, the first solution of the system is x = 1 and y = 5.

Verification

To verify this solution, substitute the values of x and y into the remaining equations and check if they hold true.

For equation 2): -6(1) + 3(5) = 9 -6 + 15 = 9 9 = 9 (True)

For equation 4): 2(1) + 2(5) = 12 2 + 10 = 12 12 = 12 (True)

For equation 5): 1 - 0.5(5) = 5 1 - 2.5 = 5 -1.5 = 5 (False)

Since the last equation does not hold true, the solution (x = 1, y = 5) is not valid for equation 5).

Conclusion

In conclusion, the given system of equations does not have a valid solution that satisfies all the equations simultaneously. The solution (x = 1, y = 5) only satisfies some of the equations but not all of them.