Question

1)8x+3y=-21 4x-6y=-182)3x-2y=55x+4y=1

Answer 1

1).
Решение способом сложения,
- 8х + 12у = 36 
8х - 8х + 3у + 12у = 36 - 21 
15у = 15 
у = 1 
4х - 6 = - 18 
4х = - 12 
Х = - 3 
Ответ (-3 ; 1).

2) 3х - 2у = 5

5х + 4у = 1

Умножим первое уравнение на 2.

6х - 4у = 10

5х + 4у = 1

Складываем 

6х + 5х = 11х

- 4 у + 4 у = 0

10 +1 = 11

Отсюда

11х + 0 = 11

х = 1

Чтобы найти у подставим значение х

5 * 1 + 4у = 1

4у= - 4

у= - 1

Ответ: (1; -1)

Answer 2

To solve the system of equations, we can use either the substitution method, elimination method, or matrix method. I'll use the elimination method to solve both systems of equations.

1. 8x + 3y = -21 4x - 6y = -18

Step 1: Multiply the first equation by 2 to make the coefficients of y in both equations equal: 2(8x + 3y) = 2(-21) 16x + 6y = -42

Now, the two equations are: 16x + 6y = -42 4x - 6y = -18

Step 2: Add the two equations to eliminate y: (16x + 6y) + (4x - 6y) = -42 - 18 20x = -60

Step 3: Solve for x: x = -60 / 20 x = -3

Step 4: Substitute the value of x into one of the original equations to solve for y: 8x + 3y = -21 8(-3) + 3y = -21 -24 + 3y = -21

Step 5: Solve for y: 3y = -21 + 24 3y = 3 y = 3 / 3 y = 1

So, the solution to the first system of equations is x = -3 and y = 1.

2. 3x - 2y = 5 5x + 4y = 1

To eliminate y, we'll multiply the first equation by 2 and the second equation by 1, so the coefficients of y become opposites:

Step 1: Multiply the first equation by 2 and the second equation by -2: 2(3x - 2y) = 2(5) -2(5x + 4y) = -2(1) 6x - 4y = 10 -10x - 8y = -2

Now, the two equations are: 6x - 4y = 10 -10x - 8y = -2

Step 2: Add the two equations to eliminate y: (6x - 4y) + (-10x - 8y) = 10 - 2 -4x - 12y = 8

Step 3: Divide the whole equation by -4 to solve for y: -4x - 12y = 8 (-4x - 12y) / -4 = 8 / -4 x + 3y = -2

Step 4: Solve for y: 3y = -2 - x y = (-2 - x) / 3

Now we have the expressions for x and y, but we don't have a unique solution since both variables depend on each other. This system of equations represents a line in a 2D plane, and there are infinite points (x, y) that satisfy the given equations.

Hence, the solution to the second system of equations is x + 3y = -2, and y = (-2 - x) / 3, where x can be any real number, and y depends on the value of x.