Question

Решите систему уравнений методом подстановки: б)6(x+y)=5-(2x+y) 3x-2y=-3y-3 Срочно!

Answer 1

Упростим второе уравнение:
3х+у=-3
выразим
у=-3-3х
упростим и подставим в первое
6х+6у-5+2х+у=0
8х+7у-5=0
8х-21-21х-5=0
-13х=26
х=-2

у=-3+6=3

Answer 2

Solution to the System of Equations using the 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 and solve for the remaining variable.

The given system of equations is: 6(x+y) = 5 - (2x+y) ...(1) 3x - 2y = -3y - 3 ...(2)

Let's solve the system step by step:

Step 1: Solve equation (1) for x in terms of y: 6(x+y) = 5 - (2x+y) 6x + 6y = 5 - 2x - y 8x = -y + 5 - 6y 8x = -7y + 5 x = (-7y + 5)/8 ...(3)

Step 2: Substitute equation (3) into equation (2): 3x - 2y = -3y - 3 3((-7y + 5)/8) - 2y = -3y - 3 (-21y + 15)/8 - 2y = -3y - 3 -21y + 15 - 16y = -24y - 24 -37y + 15 = -24y - 24 -37y + 24y = -24 - 15 -13y = -39 y = -39/-13 y = 3

Step 3: Substitute the value of y back into equation (3) to find x: x = (-7(3) + 5)/8 x = (-21 + 5)/8 x = -16/8 x = -2

Therefore, the solution to the given system of equations is x = -2 and y = 3.

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