Question

FAN AND MEDAL
Solve the following system of equations:

4x - 2y - z = -5
x - 3y + 2z = 3
3x + y - 2z = -5

(0, 1, 3)

(0, -1, 3)

(0, 1, -3)

(0, -1, -3)

Answer 1

4x - 2y - z = -5 --->(2)
x - 3y + 2z = 3
---------------
8x - 4y - 2z = -10 (result of multiplying by 2)
x - 3y + 2z = 3
---------------add
9x - 7y = - 7

x - 3y + 2z = 3
3x + y - 2z = -5
---------------add
4x - 2y = -2

9x - 7y = -7 --->(2)
4x - 2y = -2 --->(-7)
----------------
18x - 14y = -14 (result of multiplying by 2)
-28x + 14y = 14 (result of multiplying by -7)
----------------add
-10x = 0
x = 0

4x - 2y = -2
4(0) - 2y = -2
-2y = -2
y = 1

4x - 2y - z = -5
4(0) - 2(1) - z = -5
-2 - z = -5
-2 + 5 = z
3 = z

check..
x - 3y + 2z = 3
0 - 3(1) + 2(3) = 3
-3 + 6 = 3
3 = 3 (correct)

answer : (0,1,3)

Answer 2

x=3+3y-2z
4(3+3y-2z)-2y-z=-5
12+12y-8z-2y-z=-5
12+10y-9z=-5
10y-9z=-17
3(3+3y-2z)+y-2z=-5
9+9y-6z+y-2z=-5
10y-8z=-14
-9z--8z=-17--14
-z=-3
z=3
10y-8(3)=-14
10y-24=-14
10y=-14+24
y=1
x=3+3(1)-2(3)
x=3+3-6
x=0

Answer 3

guess they got it :P lol