SOLUTION: how to solve ordered triple as 6x+2y-3z=-17 7x-5y+z=72 2x+8y+3z=-21

Click here to see ALL problems on Matrices-and-determiminant

Question 914130: how to solve ordered triple as 6x+2y-3z=-17 7x-5y+z=72 2x+8y+3z=-21
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website!

Use either matrix row operations or simple successive substitutions.

If you are not yet advanced, then pick any first substitution for use of this method, starting with whichever equation you believe would be most convenient.

I'm choosing the second equation in the given system.

Use this in the first and the third equations and simplify them.

and the other equation,

You now have this system to work with:

From this system, pick an equation, solve for either variable; substitute into the other equation and solve for the single variable. NOW back substitute successively to get the values for the other two variables.

Answer by MathTherapy(10555) (Show Source):
You can put this solution on YOUR website!
how to solve ordered triple as 6x+2y-3z=-17 7x-5y+z=72 2x+8y+3z=-21

8x + 10y = - 38 ---------- Adding eqs (i) & (iii) to eliminate z ----- eq (iv)
21x - 15y + 3z = 216 ----- Multiplying eq (ii) by 3 ------ eq (v)
27x - 13y = 199 ------- Adding eqs (v) & (i) ---------- eq (vi)
270x - 130y = 1,990 ------ Multiplying eq (vi) by 10 ----- eq (vii)
104x + 130y = - 494 ------ Multiplying eq (iv) by 13 ----- eq (viii)
374x = 1,496 ------ Adding eqs (vii) & (viii)
x = , or
8(4) + 10y = - 38 ------- Substituting 4 for x in eq (iv)
32 + 10y = - 38
10y = - 38 - 32
10y = - 70
y = , or
6(4) + 2(- 7) - 3z = - 17 ------- Substituting 4 for x and - 7 for y in eq (i)
24 - 14 - 3z = - 17
10 - 3z = - 17
- 3z = - 17 - 10
- 3z = - 27
z = , or