Question

Решите систему x+y=12 x-y=5

Answer 1

Метод вычитания. От первого уравнения отнимаем второе.

х+у-х+у=12-5

2у=7

у=3.5

х+3.5=12

х=12-3.5

х=8.5

Ответ: х=8.5; у=3.5

Answer 2

To solve the system of equations, you can use the method of substitution or elimination. Let's use the elimination method to find the values of x and y.

Given the system of equations:

1. x + y = 12
2. x - y = 5

Step 1: Add the two equations to eliminate y.

(1) + (2): (x + y) + (x - y) = 12 + 5

Simplifying: 2x = 17

Step 2: Solve for x.

Divide both sides by 2: x = 17 / 2 x = 8.5

Step 3: Substitute the value of x into either equation to find y. Let's use Equation (1).

x + y = 12

Substitute x with 8.5: 8.5 + y = 12

Step 4: Solve for y.

Subtract 8.5 from both sides: y = 12 - 8.5 y = 3.5

So, the solution to the system of equations is: x = 8.5 y = 3.5