Question

X+y=3 2x-y=3 решите систему уравнений способом сложения

Answer 1

Ответ:

(2;1)

Объяснение:

х+у=3

2х-у=3

3х =  6;  х=2;  у=1

Answer 2

суммируем уравнения →

3х=6; х=6:3; х=2

2+у=3; у=3-2; у=1

Ответ: (2;1).

Answer 3

Solving the System of Equations

To solve the system of equations using the method of addition, we need to add the two equations together in a way that eliminates one of the variables. Let's solve the given system of equations:

Equation 1: x + y = 3 Equation 2: 2x - y = 3

To eliminate the variable y, we can multiply Equation 1 by 2 and add it to Equation 2:

2(x + y) + (2x - y) = 2(3) + 3 2x + 2y + 2x - y = 6 + 3 4x + y = 9

Now we have a new equation:

Equation 3: 4x + y = 9

We can solve this equation for y:

y = 9 - 4x

Now we can substitute this value of y back into Equation 1 to solve for x:

x + (9 - 4x) = 3 x + 9 - 4x = 3 -3x + 9 = 3 -3x = -6 x = 2

Substituting the value of x back into Equation 1, we can solve for y:

2 + y = 3 y = 3 - 2 y = 1

Therefore, the solution to the given system of equations is x = 2 and y = 1.

Note: The solution to the system of equations was obtained by using the method of addition, also known as the method of elimination. This method involves adding or subtracting the equations in a way that eliminates one of the variables. In this case, we added the two equations to eliminate the variable y.