Question

Помогите с решением уровнения методом замены переменной

Answer 1

например:

(xy)^2-3xy=18  заменим xy=t

t^2-3t-18=0

D=81

t=-3

t=6

тогда

t=-3

xy=-3 ; x=-3/y

4x+y=1 ; 4(-3/y)+y=1 ;

y1=-3 ; x1=1

y2=4  ; x2=-3/4

t=6

xy=6 ; x=6/y

4x+y=1 ; 4(6/y)+y=1 ;

не имеет корней

ОТВЕТ (-3/4;4) (1;-3)

 

 

Answer 2

Solving an Equation by Substitution Method

To solve an equation using the method of substitution, we substitute one variable in terms of another and then solve for the remaining variable. Let's solve the equation using this method.

The given equations are: 1) 2x + 5y = 1 (Equation 1) 2) 2x + y = 3 (Equation 2) 3) 3x + y = 4 (Equation 3)

We can solve this system of equations by substituting one variable in terms of another. Let's solve for y in terms of x using Equation 2:

From Equation 2, we have: 2x + y = 3 y = 3 - 2x (Equation 4)

Now, substitute Equation 4 into Equation 1: 2x + 5(3 - 2x) = 1 2x + 15 - 10x = 1 -8x + 15 = 1 -8x = 1 - 15 -8x = -14 x = -14 / -8 x = 7/4 or 1.75

Substitute the value of x into Equation 4 to find y: y = 3 - 2(1.75) y = 3 - 3.5 y = -0.5

Therefore, the solution to the system of equations is x = 1.75 and y = -0.5.