Question

X+3y-6z=12 3x+2y+5z = -10 2x+5y-32=6

Answer 1

Ответ:

(0;0;-2).

Пошаговое объяснение:

посмотрите решение СЛАУ методом Гаусса.

Answer 2

To solve this system of three linear equations with three variables (x, y, and z), you can use the method of substitution or elimination. I'll use the elimination method. Here are the equations:

1. $x + 3y - 6z = 12$
2. $3x + 2y + 5z = -10$
3. $2x + 5y - 32 = 6$

Let's start by eliminating one variable at a time. We'll first eliminate x:

Multiply equation 1 by 2 and equation 3 by -3 to make the coefficients of x in equations 1 and 3 equal:

1. $2x + 6y - 12z = 24$
2. $-6x - 15y + 96 = -18$

Now, add equations 1 and 3 together to eliminate x:

$(2x + 6y - 12z) + (-6x - 15y + 96) = 24 - 18$

Simplify:

$-4x - 9y - 12z = 6$

Now, we have two equations:

4. $-4x - 9y - 12z = 6$
5. $3x + 2y + 5z = -10$

Let's eliminate another variable, y. Multiply equation 4 by 2 and equation 2 by 9 to make the coefficients of y in equations 4 and 2 equal:

4. $-8x - 18y - 24z = 12$
5. $27x + 18y + 45z = -90$

Now, add equations 4 and 2 together to eliminate y:

$(-8x - 18y - 24z) + (27x + 18y + 45z) = 12 - 90$

Simplify:

$19x + 21z = -78$

Now, we have two equations:

5. $19x + 21z = -78$
6. $2x + 5y - 32 = 6$

Now, let's solve for x in equation 5:

$19x = -78 - 21z$

Divide by 19:

$x = \frac{-78 - 21z}{19}$

Now, we can substitute this expression for x into equation 3 to solve for y:

$2\left(\frac{-78 - 21z}{19}\right) + 5y - 32 = 6$

Simplify:

$\frac{-156 - 42z}{19} + 5y - 32 = 6$

Now, isolate y:

$5y = 6 + 32 + \frac{156 + 42z}{19}$

$5y = \frac{218 + 42z}{19}$

Now, divide by 5:

$y = \frac{218 + 42z}{19 \cdot 5}$

Now, you have expressions for x, y, and z in terms of z:

$x = \frac{-78 - 21z}{19}$

$y = \frac{218 + 42z}{19 \cdot 5}$

Now, you can choose a value for z, and then use these equations to find the corresponding values of x and y.