Question

15x — Оy = -21: (-5) - хтеу Ответ: бесконечное множество ретШ. Самостоятельная работа (15 мин).І вариант1. Решите способом сложения систему уравнений:x+y=5x-y=7 2.u+V=43u-5V=202) Пара чисел (-2; 3) является решением системы урав3х – by + 4 = -1,[ax + 2y +а+ b = 19.Найдите значения а и b.II вариант1. Решите способом сложения систему уравнений:|x - y= 3, (и - V = –10​

Answer 1

Ответ:

1. x=6; y=-1.

2. u=5; V=-1.

2) а=-40/3 ; b=-1/3

Объяснение:

Только в 2) в уравнении скобочка открыта и не закрыта, возможно ответ неверный.

Answer 2

I will solve the systems of equations for both variants step by step:

I. Variant 1:

1. Solve the system: x + y = 5 and x - y = 7

To use the method of addition, we add the two equations to eliminate one of the variables:

(x + y) + (x - y) = 5 + 7 2x = 12

Now, isolate x:

x = 12 / 2 x = 6

Next, substitute the value of x into one of the original equations to solve for y:

6 + y = 5 y = 5 - 6 y = -1

So the solution to the first system is x = 6 and y = -1.

2. Solve the system: u + v = 4 and 3u - 5v = 20

Again, use the method of addition:

(u + v) + (3u - 5v) = 4 + 20 4u - 4v = 24

Now, isolate u:

4u = 24 + 4v u = (24 + 4v) / 4 u = 6 + v

Since u = 6 + v, we can substitute this into the first equation to find v:

(6 + v) + v = 4 2v = 4 - 6 2v = -2 v = -2 / 2 v = -1

Now that we have v, we can find u:

u = 6 + (-1) u = 5

The solution to the second system is u = 5 and v = -1.

II. Variant 1: Solve the system: 3x - by + 4 = -1 and ax + 2y + a + b = 19

To find the values of a and b, we can use the fact that the pair of numbers (-2, 3) is a solution to the system. So, substitute these values into the two equations:

1. 3(-2) - b(3) + 4 = -1 -6 - 3b + 4 = -1 -3b = -1 + 6 - 4 -3b = 1 b = 1 / -3 b = -1/3

2. a(-2) + 2(3) + a - 1/3 = 19 -2a + 6 + a - 1/3 = 19 -a + 6 - 1/3 = 19 -a + 18/3 - 1/3 = 19 -a + 17/3 = 19 -a = 19 - 17/3 -a = 58/3 a = -58/3

So, the values of a and b are a = -58/3 and b = -1/3.

III. Variant 2: Solve the system: |x - y| = 3 and (i - V) = -10

1. |x - y| = 3

This equation has two possible cases:

Case 1: x - y = 3 Case 2: -(x - y) = 3 (which is equivalent to -x + y = 3)

Now we'll solve both cases:

Case 1: x - y = 3

Next, solve the second equation: i - V = -10

From the second equation, we get:

i = -10 + V

Now, we have two equations:

x - y = 3 i = -10 + V

Unfortunately, the system of equations is not fully specified. We don't have enough information to find the exact values of x, y, i, and V.