Question

X+y=140 (x-26)=2(y-60)решить систему управления​

Answer 1

Ответ:

х+у=140

(х-26)=2(у-60)

х=140-у

((140-у-26)=2(у-60)

114-у=2у-120

у+2у=120+114

3у=234

у=234÷3

у=78

х=140-78=62

Answer 2

To solve the system of equations, we'll first simplify the second equation and then use one of the methods to find the values of x and y. Let's proceed step by step:

1. Simplify the second equation: Distribute the 2 on the left side of the equation: (x - 26) = 2(y - 60) x - 26 = 2y - 120

2. Move all terms containing y to one side of the equation: x - 2y = -120 + 26 x - 2y = -94

Now we have a system of two equations:

1. x + y = 140
2. x - 2y = -94

There are different methods to solve this system, such as substitution, elimination, or using matrices. Let's use the elimination method to solve it:

Step 1: Multiply the first equation by 2 so that the coefficients of x in both equations will cancel each other out during the elimination process.

1. 2(x + y) = 2(140) 2x + 2y = 280

2. x - 2y = -94

Step 2: Add the equations together to eliminate the y term:

(2x + 2y) + (x - 2y) = 280 - 94 3x = 186

Step 3: Solve for x:

x = 186 / 3 x = 62

Step 4: Substitute the value of x back into one of the original equations to find y:

x + y = 140 62 + y = 140 y = 140 - 62 y = 78

So, the solution to the system of equations is x = 62 and y = 78.