Решите системы уравнений способом подстановки

1.

u+2v=7

u^2=4v=13

2.

y^2-z=3

y^2+3z=7

3.

m^2+5n=-14

m-2n=7

4.

2k-2t^2=7

3k+5t=20

1. u = 7-2v

(7-2v) ^2 + 4v - 13 = 0

49 - 28v + 4v^2 + 4v - 13 = 0

4v^2 - 24v + 36 = 0 (:4)

v^2 - 6v + 9 = 0

(v - 3) ^2 = 0

v = 3

u = 7 - 2*3 = 7-6=1

Ответ : v=3, u=1

2. z = - 3+y^2

y^2 + 3 * (y^2-3) - 7=0

y^2 + 3y^2 - 9-7 = 0

4y^2 - 16 = 0

4 * (y^2-4) = 0

y = 2 y=-2

z = 4-3=1 z = 4-3=0

Ответ : y = 2, z=1; y=-2, z=1

3. m = 7+2n

(7+2n) ^2 + 5n + 14 = 0

49 + 28n + 4n^2 + 5n + 14 = 0

4n^2 + 33n + 65 = 0

D = 1089 - 1040 = 49

n1 = - 33+7/8 = - 26/8 = - 3,25

n2 = - 33-7/8 = - 40/8 = - 5

m1 = 7 - 2 * 26/8 = 7-6,5 = 0,5

m2 = 7 - 2*5 = 7-10 = - 3

Ответ : n=-3,25, m=0,5; n=-5, m=-3

4. 2k = 7+2t^2

k = 7+2t^2/2

3 * (7+2t^2/2) + 5t - 20 = 0

6t^2 + 10t - 19 = 0

D = 784

t1 = 1,5

t2 = - 19/6

k1 = 5,75

k2 = 13 19/36