system of equations?

Question

there's 3 systems to solve. x, y, and z.

1. (-x+2y+4z=10)
2. (2x-3y-7z= -13)
3. (2x-4y-6z= -24)

show of work is required. please! thanks

Answer 1

1. -x +2y +4z=10
2. 2x -3y-7z=-13
3. 2x -4y -6z=-24 Multiply equation 1 by 2 to get equation 4
4. -2x+4y+8z=20
Now add equations 2 and 4 to get equation 5,
and add equations 3 and 4 to get equation 6

5. y+z=7
6. 2Z=-4 so z=-2

Put -2 in for z in equation 5 and get y + -2 = 7 Add 2 to both sides

y=9

Now put -2 for z, and 9 for y in either equation 1,2 or 3

I'll put it in equation 1, then I'll check my three answers in 2 (or 3)

-x+2y+4z=10
-x +2(9) +4(-2)=10
-x +18 + (-8) =10
-x +10 =10
-x =0
x=0

Check in equation 2: 2(0) -3(9) -7(-2) = -13
0-27 + 14 = -13
-13=-13

Answer 2

OK Augusta, I'll answer your question. I expect a cookie!

x=2y+4z-10 (from equation 1)
4y+8z-20-3y-7z=-13 (combining equations 1 & 2)
y=-z+7
4y+8z-20-4y-6z=-24 (combining equations 1 & 3)
2z=-4 (simplifying)
z=-2
y=2+7=9
x=2y+4z-10
x=18-8-10=0

check,

2x-4y-6z=-24
0-36+12=-24 Good, so x=0, y=9, z=-2

Answer 3

-x + 2y + 4z = 10
2x - 3y - 7z = -13
2x - 4y - 6z = -24

-x + 2y + 4z = 10
2x - 4y - 6z = -24

Multiply top by 2

-2x + 4y + 8z = 20
2x - 4y - 6z = -24

2z = -4
z = -2

2x - 3y - 7(-2) = -13
2x - 3y + 14 = -13
2x - 3y = -27
-3y = -2x - 27
y = (2/3)x + 9

-x + 2((2/3)x + 9) + 4(-2) = 10
-x + (4/3)x + 18 - 8 = 10
(-3/3)x + (4/3)x + 10 = 10
(1/3)x = 0
x = 0

y = (2/3)(0) + 9
y = 9

x = 0
y = 9
z = -2

Answer 4

Multiply (1) by 2:
(4). -2x + 4y + 8z = 20

Add (3) and (4):
2x -4y -6z -2x + 4y +8z = -24 + 20
2z = -4
z = -2

Substitue z into (2) and (3):
2x - 3y +14 = -13
(5) 2x - 3y = -27

2x - 4y + 12 = -24
(6) 2x - 4y = -36

Subtract (6) from (5):
2x - 3y -2x + 4y = -27 + 36
y = 9

Substitute y into (6):
2x - 36 = -36
x = 0