SOLUTION: Question #1 6x + 5y +2z = 830 3x + 7y+4z=820 2z-22=x HELP!

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Question 217872: Question #1
6x + 5y +2z = 830
3x + 7y+4z=820
2z-22=x
HELP!
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
6x + 5y +2z = 830
3x + 7y+4z=820
2z-22=x
------------
Since x is already given in terms of z (in the 3rd eqn), sub for x in the other 2 equations.
6x + 5y +2z = 830
3x + 7y+4z=820
-------------
6(2z-22) + 5y + 2z = 830
5y + 14z = 962 Eqn A
------------
3(2z-22) + 7y + 4z = 820
7y + 10z = 886 Eqn B
--------------
Get the same coefficient for y by multiplying Eqn A by 7 and Eqn B by 5
------------
35y + 98z = 5810 A times 7
35y + 50z = 4430 B times 5
---------------- Subtract
0y + 48z = 1380
z = 1380/48
z 115/4 One answer done
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Sub for z into Eqn A (or B, same result)
5y + 14z = 962 Eqn A
5y + 14*115/4 = 962
5y = 962 - 805/2 = 1119/2
y = 1119/10 = 111.9
--------------------
Sub for y and z into any of the 3 original eqns to find x
6x + 5y +2z = 830
6x + 5*1119/10 + 2*115/4 = 830
6x = 4260/6
x = 710
-------

Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!
Question #1
6x + 5y +2z = 830 ------ (i)
3x + 7y+4z=820 ---------(ii)
2z-22=x ---------------(iii)
HELP!

Substitute 2Z - 22 for x in eq (i)

6x + 5y +2z = 830

6(2z - 22) + 5y + 2z = 830

12z - 132 + 5y + 2z = 830

5y + 14z = 962 ---------- (iv)


Substitute 2Z - 22 for x in eq (ii)

3x + 7y + 4z = 820

3(2z - 22) + 7y + 4z = 820

6z - 66 + 7y + 4z = 820

7y + 10z = 886 ---------- (v)


We now have 2 equations with 2 variables

5y + 14z = 962 ---------- (iv)
7y + 10z = 886 ---------- (v)

35y + 98z = 6,734 ---------- (vi) ------ Multiplying eq (iv) by 7
- 35y - 50z = - 4,430 ---------- (vii)------ Multiplying eq (v) by - 5

Add eq (vi) and (vii) to get: 48z = 2,304

z = 2304%2F48 = highlight_green%2848%29

Substitute 48 for z in eq (v): 7y + 10z = 886 ---------- 7y + 10(48) = 886

7y + 480 = 886

7y = 406

y+=+406%2F7 = highlight_green%2858%29

Substitute 48 for z in any of the equations, but I chose eq (iii) since it's the simplest to substitute in to calculate the value of x

2z - 22 = x

2(48) - 22 = x
96 - 22 = x
x = highlight_green%2874%29