math help?

Question

how do get the solution of x,y,z

-5x+3y+z=-15
10x+2y+8z=18
15x+5y+7z=9?

thx for the help i appreciate it =)

Answer 1

Solve,

-5x + 3y + z = -15 ... (1)

10x + 2y + 8z = 18 ... (2)

15x + 5y + 7z = 9 ... (3)


Take 2 x (1) + (2),

8y + 10z = -12 ... (4)


Take 3 x (1) + (3),

14y + 10z = -36 ... (5)


Next, take (5) - (4)

6y = -24

y = -4


Substitute y = -4 into (4)

8(-4) +10z = -12

10z = 20

z = 2


Substitute y = -4 and z = 2 into (2)

10x + 2(-4) + 8(2) = 18

10x = 10

x = 1


Answers x = 1, y = -4 and z = 2

Answer 2

1). Equation -5x + 3y + z = - 15
2). Equation 10x + 2y + 8z = 18
3). Equation 15x + 7y + 7z = 0

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Elimination of x 1st and 2nd equation

2(-5) + 2(3y) + 2(z) = 2(- 15)

Multiplying both sides by 2 for the first (1st) equation

-10x + 6y + 2z = -30
10x + 2y + 8z = 18
------------------------------

8y + 10z = - 12

- - - - - - - - - - - - - - - - -- - -- - - - - - - - - - - - - - - - - - -

Elimination of x 1st and 3rd equation

3(-5x) + 3(3y) + 3(z) = 3 (- 15)

Multiplying 3 on both sides of the equation

-15x + 9y + 3z = - 45
15x + 5y + 7z = 9
-----------------------------
14y + 10z = - 36

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Solving for y. Elimination of z

- 1(14y) + ( -1)(10z) + = -1(-36)
-14y + (-10z ) = 36

8y + 10z = -12
-14y -10z = 36

-6y = 24

-6y/-6/ = 24/- 6

Dividing - 6 from both sides

y = -4

Insert the y value into thy y position

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Solving for z

8y + 10z = -12

8(-4) + 10 z = - 12

-32 + 10z = - 12
+32 +32

adding + 32 to both sides

10z = 20

10z/10 = 20/10

dividing 10 from both sides

z = 2

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Solving for x

Y = - 4
Z = 2

insert the above values into the y and z positions

- - - - - - - - - - - - - - - - - - - - -

First (1st) equation

-5x + 3y + z = -15

-5x +3(- 4) + 2 = -15

-5x + (-12) + 2 = - 15

-5x -12 + 2 = -15

-5x --10 = - 15
+10 +10

Adding + 10 to both sides

-5x = -5

-5x/-5 = -5/-5

Dividing - 5 from both sides

x = 1

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Proof

x = 1
y = -4
z = 2

insert the above values into the x, y and z poditions

- - - - - - - - - - - - - - - - -

1st equation PROOF

-5x + 3y + z = - 15

-5(1) + 3(- 4) + 2 = -15

-5 + (-12) + 2 = - 15
-5 -12 + 2 = -15

-17 + 2 = -15

-15 = - 15

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Proof for second (2nd) equation

2nd equation

10x + 2y + 8z = 18

10(1) + 2(-4) + 8(2) = 18

10 + (-8) + 16 = 18

10 - 8 + 16 = 18

2 + 16 = 18

18 = 18

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Proof for third (3rd) equation

15x + 5y + 7z = 9

15(1) + 5(- 4) + 7(2) = 9

15 + (- 20) + 14 = 9

15 - 20 + 14 = 9

-5 + 14 = 9

9 = 9

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The answer for x, y, and z

x = 1
y = - 4
z = 2

Answer 3

-5x + 3y + z = -15
10x + 2y + 8z = 18
15x + 5y + 7z = 9

-5x + 3y + z = -15
10x + 2y + 8z = 18

Multiply the top by 2

-10x + 6y + 2z = -30
10x + 2y + 8z = 18

8y + 10z = -12
4y + 5z = -6
5z = -4y - 6
z = (-4/5)y - (6/5)

15x + 5y + 7z = 9
15x + 5y + 7((-4/5)y - (6/5)) = 9
15x + 5y - (28/5)y - (42/5) = 9
75x + 25y - 28y - 42 = 45
75x - 3y - 42 = 45
75x - 3y = 87
25x - y = 29
25x = y + 29
x = (1/25)y + (29/25)

-5x + 3y + z = -15
-5((1/25)y + (29/25)) + 3y + ((-4/5)y - (6/5)) = -15
(-1/5)y - (29/5) + 3y - (4/5)y - (6/5) = -15
-y - 29 + 15y - 4y - 6 = -75
10y - 35 = -75
10y = -40
y = -4

z = (-4/5)y - (6/5)
z = (-4/5)(-4) - (6/5)
z = (16/5) - (6/5)
z = (16 - 6)/5
z = (10/5)
z = 2

x = (1/25)y + (29/25)
x = (1/25)(-4) + (29/25)
x = (-4/25) + (29/25)
x = (-4 + 29)/25
x = (25/25)
x = 1

x = 1
y = -4
z = 2

Answer 4

Addition and substitution.

-5x + 3y + z = -15
z = 5x - 3y - 15

10x + 2y + 8(5x - 3y - 15) = 18
10x + 2y + 40x - 24y - 120 = 18
50x - 22y = 138

15x + 5y + 7(5x - 3y - 15) = 9
15x + 5y + 35x - 21y - 105 = 9
50x - 16y = 114

-6y = 24
y = -4

50x - 16(-4) = 114
50x + 64 = 114
50x = 50
x = 1

-5(1) + 3(-4) + z = -15
-5 - 12 + z = -15
-17 + z = -15
z = 2

(1, -4, 2) is the solution.

Answer 5

add:

(-5x+3y+z=-15)+
(10x+2y+8z=18)+
(15x+5y+7z=9)=

20x+10y+16z=12.

That's all i can do. Find x, y, and z for yourself. Sorry!

Answer 6

You want to use your system of equations to solve for each variable. Use the first equation to get a value for z in terms of x and y. Then substitute that value in to the other two equations. Now you have two equations with two variables. Pick one and find a value for it in terms of the other one then substitute that in to your third equation. Now you have one equation with one variable. Solve for that variable and then plug that value back in to your two variable equation and solve for the other variable. Now you have values for x and y. Plug those values back in to the first equation and solve for z.

You can also solve this using matrices, but its late and I really need to get to bed.

Answer 7

the answer is 69er dude

Answer 8

Dude, its summer.