Question

I am in desperate need of assistance!!! if i dont get this answer right theyre going to take everything i have, even my dog, so please help me out. your help will be very much appreciated and i will forever be grateful for a stranger to help me.Explain what method you would use to solve the following system:

3x + 4y – 5z = -3
-5x -2y + 6z = 5
4x – 8y + 3z = -10


please if you can explain the steps. thank you very much!!!!!!

Answer 1

{x,y,z} = {-3,-1,-2}

Explanation:

// Solve equation [3] for the variable z

[3] 3z = -4x + 8y - 10

[3] z = -4x/3 + 8y/3 - 10/3

// Plug this in for variable z in equation [1]

[1] 3x + 4y - 5•(-4x/3+8y/3-10/3) = -3

[1] 29x/3 - 28y/3 = -59/3

[1] 29x - 28y = -59

// Plug this in for variable z in equation [2]

[2] -5x - 2y + 6•(-4x/3+8y/3-10/3) = 5

[2] -13x + 14y = 25

// Solve equation [2] for the variable y

[2] 14y = 13x + 25

[2] y = 13x/14 + 25/14

// Plug this in for variable y in equation [1]

[1] 29x - 28•(13x/14+25/14) = -59

[1] 3x = -9

// Solve equation [1] for the variable x

[1] 3x = - 9

[1] x = - 3

// By now we know this much :

x = -3

y = 13x/14+25/14

z = -4x/3+8y/3-10/3

// Use the x value to solve for y

y = (13/14)(-3)+25/14 = -1

// Use the x and y values to solve for z

z = -(4/3)(-3)+(8/3)(-1)-10/3 = -2