Question

Решите систему линейных уравнений способом сложения {x+y=5,{2x+2y=6

Answer 1

Домножим первое уравнение системы на (-2), получим
-2x-2y = -10, теперь сложим это со вторым уравнением из системы:
(-2x - 2y)+2x+2y = -10+6,
0 = -4. Это ложное равенство, оно никогда не выполняется, ни при каком иксе, игреке. Что означает, что множество решений - это пустое множество. Решений нет.

Answer 2

Solution to the System of Linear Equations

To solve the system of linear equations using the method of addition, we have the following equations:

Equation 1: x + y = 5 Equation 2: 2x + 2y = 6

To solve this system, we can multiply Equation 1 by 2 to make the coefficients of x in both equations the same. This will allow us to eliminate x when we add the two equations together.

Multiplying Equation 1 by 2, we get: 2(x + y) = 2(5) 2x + 2y = 10

Now we can add Equation 2 and the modified Equation 1 together: (2x + 2y) + (2x + 2y) = 6 + 10 4x + 4y = 16

Dividing both sides of the equation by 4, we get: x + y = 4

Now we have a new equation: Equation 3: x + y = 4

To solve for x and y, we can subtract Equation 3 from Equation 1: (x + y) - (x + y) = 5 - 4 0 = 1

Since 0 does not equal 1, this means that the system of equations is inconsistent and has no solution. The two original equations are parallel lines that do not intersect.

Therefore, the system of linear equations: x + y = 5 2x + 2y = 6

does not have a solution.