Question

3x - y = 2x+2y -z= 22x -y +2z =2это всё в системе

Answer 1

Решал методом Гауса,потом записал систему в стандартном виде ,решил подстановкой

Answer 2

To solve the given system of linear equations:

1. 3x - y = 2
2. 2x + 2y - z = 22
3. 22x - y + 2z = 2

There are multiple methods to solve systems of linear equations, such as substitution, elimination, or matrix methods. I'll demonstrate the elimination method.

Step 1: Let's start by eliminating one variable from two of the equations. To eliminate 'y', we can add the first equation to the second equation.

Adding equation (1) and equation (2): (3x - y) + (2x + 2y) = 2 + 22 5x + y = 24

Step 2: Now let's eliminate 'y' from equation (3). To do this, we can subtract the first equation from the third equation.

Subtracting equation (1) from equation (3): (22x - y + 2z) - (3x - y) = 2 - 2 19x + 2z = 0

Step 3: We now have two equations:

1. 5x + y = 24
2. 19x + 2z = 0

Step 4: Now we can solve this system of two equations. Let's solve equation (1) for 'y':

5x + y = 24 y = 24 - 5x

Step 5: Substitute the expression for 'y' in terms of 'x' into equation (2):

19x + 2z = 0 19x + 2z = 0 19x + 2(24 - 5x) = 0 19x + 48 - 10x = 0 9x = -48 x = -48 / 9 x = -16 / 3

Step 6: Now that we have the value of 'x', we can find the value of 'y' using equation (1):

5x + y = 24 5(-16 / 3) + y = 24 -80 / 3 + y = 24 y = 24 + 80 / 3 y = (72 + 80) / 3 y = 152 / 3

Step 7: Finally, we can find the value of 'z' using equation (3):

22x - y + 2z = 2 22(-16 / 3) - 152 / 3 + 2z = 2 -352 / 3 + 2z = 2 2z = 2 + 352 / 3 2z = (6 + 352) / 3 2z = 358 / 3 z = 358 / (3 * 2) z = 358 / 6 z = 179 / 3

So, the solution to the system of equations is: x = -16/3 y = 152/3 z = 179/3