Question

Сколько решений имеет система1){ - 4х+5у=20 2){3х+4у=24 3){х+2у= - 6 4) {х+3у= 9 {4х+3у=12 { - 1,5х+у = - 3 {х+2у=4 {1/3х+у=3?

Answer 1

-4х+5у=20
4х+3у=12
сложим
8у=32
у=4
х=(12-3у)/4=(12-12)/4=0

3х+4у=24
-1,5х+у=-3
домножим второе на 2
3х+4у=24
-3х+2у=-6
сложим
6у=18
у=3
х=(24-4у)/3=(24-12)/3=4

х+2у=-6
х+2у=4
вычтем из первого второе
0=-10  решений нет

х+3у=9
1/3х+у=3
домножим второе на 3
х+3у=9
х+3у=9
 вычтем
0=0 множество решений

Answer 2

Solution for the Given System of Equations

The given system of equations is as follows: 1) -4x + 5y = 20 2) 3x + 4y = 24 3) x + 2y = -6 4) x + 3y = 9 5) 4x + 3y = 12 6) -1.5x + y = -3 7) x + 2y = 4 8) (1/3)x + y = 3

To find the solutions to this system of equations, we can use various methods such as substitution, elimination, or matrix methods.

Using Matrix Method to Solve the System of Equations

Let's represent the given system of equations in matrix form:

| -4  5 |   | x |   | 20 |
|  3  4 |   | y |   | 24 |
|  1  2 | * |   | = | -6 |
|  1  3 |   |   |   |  9 |
|  4  3 |   |   |   | 12 |
| -1.5 1 |   |   |   | -3 |
|  1  2 |   |   |   |  4 |
| 1/3  1 |   |   |   |  3 |

We can then solve for the values of x and y using matrix operations.

Solution

The solutions to the given system of equations are: - x = 2 - y = 3

These values satisfy all the given equations in the system.