Question

X - y=11 x² + y²=173​

Answer 1

Объяснение:

$\left \{ {x-y=11} \atop {x^2+y^2=173}} \right. \ \ \ \ \left \{ {{y=x-11} \atop {x^2+(x-11)^2=173}} \right. \ \ \ \ \left \{ {{y=x-11} \atop {x^2+x^2-22x+121=173}} \right.\ \ \ \ \left \{ {{y=x-11} \atop {2x^2-22x-52=0\ |:2}} \right. \\\left \{ {{y=x-11} \atop {x^2-11x-26=0}} \right.\ \ \ \ \left \{ {{y=x-11} \atop {D=225}\ \ \sqrt{D}=15 } \right. \ \ \ \ \left \{ {{y_1=2\ \ y_2=-13} \atop {x_1=13\ \ x_2=-2}} \right. .$

Ответ: (13;2), (-2;-13).

Answer 2

To solve the system of equations:

1. X - y = 11
2. x² + y² = 173

We can use the substitution method to eliminate one variable. Let's solve equation 1 for X:

X = y + 11

Now substitute this value of X into equation 2:

(y + 11)² + y² = 173

Expand the equation:

y² + 22y + 121 + y² = 173

Combine like terms:

2y² + 22y + 121 - 173 = 0

Simplify:

2y² + 22y - 52 = 0

Divide the equation by 2 to simplify:

y² + 11y - 26 = 0

Now we can solve this quadratic equation. You can either factor it or use the quadratic formula. Let's use the quadratic formula:

y = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = 11, and c = -26. Substituting the values:

y = (-11 ± √(11² - 4(1)(-26))) / (2(1))

Simplifying:

y = (-11 ± √(121 + 104)) / 2 y = (-11 ± √225) / 2 y = (-11 ± 15) / 2

This gives us two possible values for y:

y₁ = (-11 + 15) / 2 = 2 y₂ = (-11 - 15) / 2 = -13

Now substitute these values back into equation 1 to find the corresponding values of X:

For y = 2: X = y + 11 = 2 + 11 = 13

For y = -13: X = y + 11 = -13 + 11 = -2

Therefore, the solution to the system of equations is (X, y) = (13, 2) and (-2, -13).