Question

Решите методом подстановки систему уравнений {x+y=-6 {3x-y=8

Answer 1

Y=-x-6; 3x+x+6=8; 4x=2; x=2/4; x=0.5
y=-0.5-6; y=-6.5

Answer 2

Solving the System of Equations using the Substitution Method

To solve the system of equations using the substitution method, we need to find the values of x and y that satisfy both equations:

Equation 1: x + y = -6 (1) Equation 2: 3x - y = 8 (2)

We can start by solving Equation 1 for one variable and then substituting that expression into Equation 2.

From Equation 1, we can solve for x: x = -6 - y (3)

Now, substitute the expression for x from Equation 3 into Equation 2: 3(-6 - y) - y = 8

Let's simplify this equation step by step:

- Distribute the 3: -18 - 3y - y = 8

- Combine like terms: -4y - 18 = 8

- Add 18 to both sides: -4y = 26

- Divide both sides by -4: y = -26/4 y = -6.5

Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:

x + (-6.5) = -6

- Combine like terms: x - 6.5 = -6

- Add 6.5 to both sides: x = -6 + 6.5 x = 0.5

Therefore, the solution to the system of equations is x = 0.5 and y = -6.5.

Solution:

The solution to the system of equations {x + y = -6, 3x - y = 8} using the substitution method is x = 0.5 and y = -6.5.

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