Question

Решите на множестве действительных чисел методом подстановки систему уравнений :{x-y=2 {2x-3y=2 б){x+y=6 {3x-5y=2

Answer 1

1)x=y+2
2y+4-3y=2
-y=-2
y=2
x=4
(4;2)
2)x=6-y
18-3y-5y=2
-8y=-16
y=2
x=4
(4;2)

Answer 2

Solving the System of Equations by Substitution Method

To solve the system of equations using the method of substitution, we will substitute one equation into the other to eliminate one variable. Let's solve the given system of equations:

Equation 1: x - y = 2 (1) Equation 2: 2x - 3y = 2 (2) Equation 3: x + y = 6 (3) Equation 4: 3x - 5y = 2 (4)

We can start by solving Equation 1 for x: x = y + 2

Now, we substitute this value of x into Equation 2: 2(y + 2) - 3y = 2 2y + 4 - 3y = 2 -y + 4 = 2 -y = 2 - 4 -y = -2 y = 2

Substituting the value of y = 2 into Equation 3: x + 2 = 6 x = 6 - 2 x = 4

Therefore, the solution to the given system of equations is x = 4 and y = 2.

Note: The solution to the system of equations is x = 4 and y = 2.