Question

Система уравнений x+2y=4 x^+xy=y-5 У меня почему-то дискриминант не тот получается, может вы сможете?

Answer 1

Х+2у=4
2у=4-х
у=2-0.5х
х²+х(2-0.5х)=2-0.5х-5
х²+2х-0.5х²=-0.5х-3
0.5х²+2х+0.5х+3=0
0.5х²+2.5х+3=0(×2)
х²+5х+6=0
D=25-4×6×1=25-24=1
x(1)=-5-1/2=-6/2=-3
x(2)=-5+1/2=-4/2-2
y(1)==2-0.5×(-3)=2+1.5=3.5
y(2)=2-0.5×(-2)=2+1=3

Answer 2

Solving the System of Equations

To solve the system of equations x + 2y = 4 and x^2 + xy = y - 5, we can use the substitution method or the elimination method. Let's use the substitution method to solve this system.

First, we can solve the first equation for x: x = 4 - 2y.

Now, we can substitute this value of x into the second equation: (4 - 2y)^2 + (4 - 2y)y = y - 5.

Expanding and simplifying this equation will give us the value of y. Once we have the value of y, we can substitute it back into the equation x = 4 - 2y to find the value of x.

Let's proceed with these calculations to find the values of x and y.

Calculating the Discriminant

The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula Δ = b^2 - 4ac. In the context of the given system of equations, the discriminant may be involved in the process of solving for the values of x and y.

Let's calculate the discriminant for the quadratic equation obtained from the substitution of x in terms of y and proceed with the solution.

I'll now perform the calculations to find the values of x and y and calculate the discriminant for the quadratic equation.