# Linear algebra problem

**Please solve this linear algebra problem for x, y and z.****Please show all of the steps.****51x + 8y + 37z = 22****99x + 27y + 44z = 83****102x + 96y + 158z = 1096**

Let's solve this system of linear equations:

- $51x+8y+37z=22$
- $99x+27y+44z=83$
- $102x+96y+158z=1096$

We can solve the system of equations using elimination.

Steps to solve:

**1. Eliminate y:** Multiply the top equation by -3 and the second equation by 4. Add the top and bottom equations. $−153x−24z=−130$ $396x+108z=332$ $243x+84z=202$

**2. Eliminate z:** Multiply the top equation by -1. Add the top and bottom equations. $243x=−332$ $x=−243332 $

**3. Substitute x back into the top equation:** $51(−243332 )+8y+37z=22$ $−70y+37z=22$

**4. Eliminate y:** Multiply the top equation by 19. $−1330y+703z=418$

**5. Substitute z back into the top equation:** $−1330y+703(27117517 )=418$ $y=13555138784 $

**6. Substitute x and y back into the top equation:** $51(−243332 )+13555138784 +37z=22$ $z=27117517 $

**Answer:**

$x=−129571/40665 $

$y=138784/13555 $

$z=7517/2711 $