Question

Розв'яжіть систему рівнянь методом підстановки: { у-2х=5 та {ху=18

Answer 1

Ответ:

{y-2x=5

{у=5+2х

2)xy=18

x•(5+2x)=18

5x+2x^2=18

2x^2+5x-18=0

D=25+144=169=13

x1=-5+13/4=2

x2=-5-13/4=-18/4=-9/2=-4.5

Подставляем х1=2:

2•у=18

у=9

Подставляем х2=-4.5:

-4.5y=18

y=18:(-4.5)=180:(-45)=-4

Ответ: (2;9) , (-4.5;-4)

(х1;у1) , (х2;у2)

Answer 2

Sure! Let's solve the system of equations using the method of substitution.

The given system of equations is: у - 2х = 5 ----(1) ху = 18 ----(2)

To solve this system, we'll solve one equation for one variable and substitute it into the other equation.

Let's solve equation (1) for у: у = 5 + 2х

Now we'll substitute this value of у into equation (2): х(5 + 2х) = 18

Expanding the equation, we get: 5х + 2х^2 = 18

Rearranging the equation, we have: 2х^2 + 5х - 18 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = 5, and c = -18. Substituting these values into the quadratic formula, we get:

x = (-5 ± √(5^2 - 4 * 2 * -18)) / (2 * 2)

Simplifying further: x = (-5 ± √(25 + 144)) / 4 x = (-5 ± √169) / 4 x = (-5 ± 13) / 4

Now we have two possible values for x: x1 = (-5 + 13) / 4 = 8/4 = 2 x2 = (-5 - 13) / 4 = -18/4 = -4.5

Now let's substitute these values of x back into equation (1) to find the corresponding values of у:

For x = 2: у = 5 + 2 * 2 = 5 + 4 = 9

For x = -4.5: у = 5 + 2 * (-4.5) = 5 - 9 = -4

Therefore, the solutions to the given system of equations are: (x, у) = (2, 9) and (x, у) = (-4.5, -4).

So, the system of equations у - 2х = 5 and ху = 18 is solved using the method of substitution and the solutions are (2, 9) and (-4.5, -4).