Math Question?

Question

not sure how to solve this? any help is appreciated!

Solve the system of equations.

2x-2y+4z=2
4x+2y-2z=-10
6x+4y-2z=-16

Answer 1

Multiply the last equation by -1

-6x - 4y + 2z = 16

Compare to second equation:

-6x - 4y + 2z = 16
4x + 2y - 2z = -10

Add the equations together

-2x - 2y = 6

You have eliminated z from the equations. You now need to eliminate it from two other equations.

Multiply second equation by 2:
8x + 4y - 4z = -20

And compare to first equation:
8x + 4y - 4z = -20
2x - 2y + 4z = 2

Add.

10x + 2y = -18

Now, compare to the other equation.

10x + 2y = -18
-2x - 2y = 6

Add the equations together.

8x = -12

x = -1.5

-2x - 2y = 6
-2(-1.5) -2y = 6
3 - 2y = 6
-2y = 3
y = -1.5

Substitute the x and y values into one of the original equations to solve for z:

2x - 2y + 4z = 2
2(-1.5) - 2(-1.5) + 4z = 2
-3 + 3 + 4z = 2
4z = 2
z = 0.5

X = -1.5
Y = -1.5
Z = 0.5

Check by substituting into the original three equations.

Answer 2

2x-2y+4z=2
4x+2y-2z=-10
6x+4y-2z=-16
to solve for x
divide the first equation by 2
x-y+2z=1
then add -(-y+2z) to both sides of the equation
now we know x=1+y-2z so we can plug that in for x
4(1+y-2z )+2y-2z=-10 simplify
4+4y-8z+2y-2z=-10 simplify
4+6y-10z=-10 simplify
6y-10z=-14
solve for y
y= (-14+10z)/6
so plug x and y into the last equation to solve for z
6(1+((-14+10z)/6)-2z )+4((-14+10z)/6)-2z=-16
and keep going from there till you get numbers for x,y and z
then make sure they fit all three equations. I might do more on this later. I'm dyslexic so don't be surprised if I made a mistake.

Answer 3

Value of z:
2x - 2y + 4z = 2
4z = 2 - 2x + 2y
z = 1/2 - 1/2x + 1/2y

Value of y:
6x + 4y - 2z = - 16
6x + 4y - 2(1/2 - 1/2x + 1/2y) = - 16
6x + 4y - 1 + x - y = - 16
7x + 3y - 1 = - 16
3y = - 15 - 7x
y = (15 - 7y)/ 3
y = - 5 - 7/3x

Value of z:
z = 1/2 - 1/2x + 1/2(- 5 - 7/3x)
z = 1/2 - 1/2x - 5/2 - 7/6x
z = - 2 - 5/3x

Value of x:
6x + 4y - 2z = - 16
6x + 4(- 5 - 7/3x) - 2(- 2 - 5/3x) = - 16
6x - 20 - 28/3x + 4 + 10/3x = - 16
There is no further solution to this problem.

Answer 4

You have three equations in three unknowns. Well, we'll do it the old-fashioned way by eliminating one variable from these equations, thus creating two equations in two unknowns. The process is repeated until you have one of the unknowns; then you work your way back and compute the others.

For example:

Multiply the first equation by -2 to get

-4x +4y -8z = -4

Add it to the second

4x + 2y -2z = -10

to get

6y -10z = -14

Now multiply the second equation by -3 and the third by 2. Add them together to eliminate x. You now have a second equation in y and z. Combine that with the previous result to solve for y and z, then x.

Answer 5

2x=2y -4z+2
x = y-2z+1
6y-12z +6 +4y-2z= -16
10 Y-14Z=-22
5Y=7Z-8

Answer 6

Find a greatest common multiple....I guess?

12x-12y+24z = 12
12x+ 6y - 6z = - 30
12x + 8y - 4z = -32

2y + 14z = -50

And so on...

Answer 7

2x-2y+4z=2
+4x+2y-2z=-10
-----------------------
6x + 2z = -8

4x+2y-2z=-10 --->>> -8x - 4y + 4z = 20

-8x - 4y + 4z = 20
+6x+4y-2z=-16
----------------------
-2x + 2z = 4


6x + 2z = -8
-(-2x + 2z = 4)
--------------------
8x = -12
x = -12/8 = -3/2 = -1.5

Can you go back and figure out y and z now?

I hope this helps!

Answer 8

Are you allowed to use Matrices to solve this problem?

Answer 9

Is this 3 equations, or one big one ??

xo

Answer 10

x = (- 1.5)
y = (- 1.5)
z = 0.5