SOLUTION: how do I solve -x-5y+z=17 -x-y+z=1 2x+5y-3z=-10

Question 1116288: how do I solve -x-5y+z=17
-x-y+z=1
2x+5y-3z=-10
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
How, depends what you know.

R2-R1 for new R2;
R3-2R1 for new R3;

-------two linear equations, two unknown variables

--------two of the variables solved - and you can finish the remaining variable however you want.

(not the only way to solve)
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
how do I solve -x-5y+z=17
-x-y+z=1
2x+5y-3z=-10

- x - 5y + z = 17 ------- eq (i)
- x - y + z = 1 --------- eq (ii)
2x + 5y - 3z = - 10 ----- eq (iii)
4y = - 16 -------- Subtracting eq (i) from eq (ii)
Right away you can see that
- x - 5(- 4) + z = 17 ------- Substituting - 4 for y in eq (i)
- x + 20 + z = 17
- x + z = - 3 ------- eq (iv)
2x + 5(- 4) - 3z = - 10 ------- Substituting - 4 for y in eq (iii)
2x - 20 - 3z = - 10
2x - 3z = 10 ------- eq (v)
- 3x + 3z = - 9 ------- Multiplying eq (iv) by 3 ------ eq (vi)
- x = 1 ------- Adding eqs (v) & (vi)

I leave it to you to find z
By the way. z CAN NEVER = 28, as YOU-KNOW-WHO will have you believe!
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