Question

Решите систему уравнений,используя способ подстановки {x=3-y {y2-x=39 {x2+y=14 {y-x=8

Answer 1

Ваша задача решена ответ в вложение

Answer 2

Solving the System of Equations using Substitution

To solve the system of equations using the method of substitution, we'll start by solving one of the equations for one variable and then substitute that expression into the other equations.

Given system of equations: 1. \( x = 3 - y \) (Equation 1) 2. \( y^2 - x = 39 \) (Equation 2) 3. \( x^2 + y = 14 \) (Equation 3) 4. \( y - x = 8 \) (Equation 4)

Solving for x in terms of y

From Equation 4, we can express \( x \) in terms of \( y \): \[ x = y - 8 \]

Substituting x in terms of y into other equations

Substitute the expression for \( x \) from Equation 1 into Equations 2 and 3: 1. Substitute \( x = 3 - y \) into Equation 2: \[ y^2 - (3 - y) = 39 \] \[ y^2 - 3 + y = 39 \] \[ y^2 + y - 42 = 0 \]

2. Substitute \( x = 3 - y \) into Equation 3: \[ (3 - y)^2 + y = 14 \] \[ 9 - 6y + y^2 + y = 14 \] \[ y^2 - 5y - 5 = 0 \]

Solving the Quadratic Equations

We have obtained two quadratic equations in terms of \( y \). We can solve these equations to find the values of \( y \).

After solving for \( y \), we can substitute the values back into the equation \( x = 3 - y \) to find the corresponding values of \( x \).

I hope this helps! Let me know if you need further assistance.