SOLUTION: 4x-5y+z=3 2x+y=4 -7y+3z=-5 solve the system's equation

Algebra ->  Systems-of-equations -> SOLUTION: 4x-5y+z=3 2x+y=4 -7y+3z=-5 solve the system's equation      Log On


   

Question 1095116: 4x-5y+z=3
2x+y=4
-7y+3z=-5
solve the system's equation
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
4x-5y+z=3
2x+y=4
-7y+3z=-5


-
2x=4-y
x=%284-y%29%2F2
-
3z=-5%2B7y
z=%287y-5%29%2F3
-

4%284-y%29%2F2-5y%2B%287y-5%29%2F3=3
multiplybothsidesby6;
12%284-y%29-30y%2B2%287y-5%29=18
6%284-y%29-15y%2B7y-5=9
24-6y-15y%2B7y=14
%28-6-15%2B7%29y=14-24
-14y=-10
y=10%2F14
highlight%28y=5%2F7%29
-
z=%287%285%2F7%29-5%29%2F3
z=0%2F3
highlight%28z=0%29

x=%284-y%29%2F2
x=%284-5%2F7%29%2F2
x=%2828%2F7-5%2F7%29%2F2
highlight%28x=23%2F14%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

4x-5y+z=3
2x+y=4
-7y+3z=-5
solve the system's equation
Piece of advice: STAY AWAY from that dude's suggested solution.
4x - 5y + z = 3 ------ eq (i)
2x + y = 4_____y = 4 - 2x ------ eq (ii)
- 7y + 3z = - 5 ------ eq (iii)
- 7(4 - 2x) + 3z = - 5 ------ Substituting 4 - 2x for y in eq (iii)
- 28 + 14x + 3z = - 5
14x + 3z = 23 ----- eq (iv)

4x - 5(4 - 2x) + z = 3 ------ Substituting 4 - 2x for y in eq (i)
4x - 20 + 10x + z = 3
14x + z = 23 ----- eq (v)
2z = 0 ------- Subtracting eq (v) from eq (iv)
highlight_green%28matrix%281%2C3%2C+z%2C+%22=%22%2C+0%29%29


- 7y + 3(0) = - 5 ------- Substituting 0 for z in eq (iii)
- 7y = - 5



matrix%281%2C3%2C+5%2F7%2C+%22=%22%2C+4+-+2x%29 ------- Substituting 5%2F7 for y in eq (ii)
matrix%281%2C3%2C+2x%2C+%22=%22%2C+4+-+5%2F7%29