Question

4х+3у-2z=4 3х+6у+3z=24 3x+2y+z=10

Answer 1

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Answer 2

It seems like you've provided a system of three linear equations with three variables: x, y, and z. To solve this system of equations, you can use methods like substitution, elimination, or matrix operations. I'll demonstrate how to solve it using the substitution method:

Given system of equations:

1. 4x + 3y - 2z = 4
2. 3x + 6y + 3z = 24
3. 3x + 2y + z = 10

Let's start by solving equation (3) for one variable and then substitute it into the other two equations:

From equation (3), we have: z = 10 - 3x - 2y

Substitute this value of z into equations (1) and (2):

Equation (1): 4x + 3y - 2(10 - 3x - 2y) = 4 4x + 3y - 20 + 6x + 4y = 4 10x + 7y = 24 Divide by 10: x + (7/10)y = 2.4 --> Equation (4)

Equation (2): 3x + 6y + 3(10 - 3x - 2y) = 24 3x + 6y + 30 - 9x - 6y = 24 -6x = -6 Divide by -6: x = 1 --> Equation (5)

Now that we have the value of x, we can substitute it back into equation (4):

1 + (7/10)y = 2.4 (7/10)y = 1.4 y = 2

Finally, substitute the values of x and y back into the equation for z that we derived earlier:

z = 10 - 3(1) - 2(2) z = 10 - 3 - 4 z = 3

So, the solution to the system of equations is x = 1, y = 2, and z = 3. You can verify this solution by substituting these values into all three original equations.