Question 217872
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  =  {{{2304/48}}} = {{{highlight_green(48)}}}


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


7y + 480 = 886


7y  =  406


{{{y = 406/7}}} = {{{highlight_green(58)}}}


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(74)}}}