last algebra question?

First, you should know that you can multiply any one of these equations through by a nonzero constant, without changing the solution. You can also add or subtract any two of the equations term by term without changing the solution.

We begin by adding equations 1 and 3 together

x+y+z = -5

x-y+4z=12

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

2x + 5z = 7 (notice that the ys cancel out)

Now we triple equation 1, and subtract equation 2 from it

3x+3y+3z= -15

2x+3y-2z = 8

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

x +5z = -23

Now we have two equations, in which we have eliminated y.

We subtract them, and solve for x.

2x + 5z = 7

x +5z = -23

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

x = 7 - (-23) = 30

It is easy to find y and z, now that we know x is 30/

x + 5z = -23

30 + 5z = -23

5z = -53

z = -(53/5) or -10.6

x + y + z = -5

30 + y + (-53/5) = -5

y = 53/5 - 30 - 5 = -24.4

So (x,y,z) = (30,-24.4,-10.6)

Eliminate one of the variables by combining one equation with the other two.

For example

x+y+z= -5

x-y+4z= 12

adding,

2x + 5z = 7 (we eliminated the y term)

and

x+y+z= -5

2x+3y-2z= 8

multiply the first by 3 to make the y terms the same and subtract.

3x+3y+3z = -15

2x+3y-2z= 8

subtracting the second from the first,

x + 5z = -23 (again we eliminated the y term)

Now combine the two resulting equations:

2x + 5z = 7

x + 5z = -23

Subtracting the second from the first will eliminate the z term and, x = 30

Now go back substituting x=30 into one of the above equations to find z.

x + 5z = -23

30 + 5z = -23

5z = - 53

z = -10.6

Now substitute the values of x and z into one of the original equations to find y.

x+y+z= -5

30 + y - 10.6 = -5

y + 19.4 = -5

y = -24.4

So, x=30, y=-24.4, z=-10.6

You can solve this using a system of equations.

Add these two equations to get rid of y first.

x+y+z=-5

x-y+4z=12

__________

2x + 5z = 7

solve for z in terms of x:

z=(7-2x)/5

Add these two equations next to get rid of z. You have to multiply the top equation by 2 in order to let the z's cancel out.

2(2x+3y-2z=8)

x-y+4z=12

4x+6y-4z=16

x-y+4z=12

___________

5x+5y = 28

Solve for y in terms of x

y=(28-5x)/5

Now you have y and z in terms of x you can use the first equation and substitute x and y.

x + (28-5x)/5 + (7-2x)/5 = -5

28-5x+7-2x+5x = -25

-2x=-60

x=30

solve for y and z by substituting x value back into y and z equations.

Hope that's the right answer and hope that helped.

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

(2) 2x+3y-2z= 8

(3) x-y+4z= 12

add 1 & 3

(4) 2x+5z=7

subtract 2 from 1a

(5) x+5z=-23

subtract 5 from 4

x=30

substitute into 4

2*30+5z=7

5z=-53

z=-10.6

substitute into 1

30+y-10.6=-5

y=10.6-5-30=-24.4

x=30

z=-10.6

y=-24.4

1) z = -5-x-y

2) put into (2): 2x+3y-2(-5-x-y) = 8 = 5y +10 ---> y = -2/5

3) put y into 1): z = -5-x+2/5 ----> z = -x-23/5

4) put this value of z and the value of y into eqn 3):

x-(-2/5)+4(-x-23/5) = 12 ----> x = -10

put this into the eqn for z: z = -x-23/5 = 5.40

y (already found) = -2/5

permit's say that N is the style of nickels, D is the style of dimes and Q is the style of quarters Then, N+D+Q=18 (18 money altogether) and each and each nickel is properly worth 5 cents, so the cost of the nickels is 5 x N cents; each and each dime is properly worth 10 cents, so the cost of the dimes is 10 X D cents and the cost of the quarters is 25 X Q cents. We then could make 3 diverse equations: one million. N+D+Q=18 2. 5N+10D+25Q=2 hundred(it particularly is $2 in cents) 3. D=2N considering there are two times as many dimes as nickels you are able to sparkling up them concurrently via substituting 2N for D in equation #one million and making Q the concern (on the left hand part via itself) Q=18-3N then you definately replace 18-3N into equation #2 for the Q and additionally replace 2N for D in equation #2: 5N + 20N + 25(18-3N) = 2 hundred in case you save on with fixing this equation it permit you already know procedures many nickels, then you certainly can artwork out something. good success.

If you are giving a 3 variable simultaneous equation, here's the answer:

x = -11.75

y = 15

z = 6.75

If you aren't giving a simultaneous equation, I have no idea what you are asking

Um, well I'm in Algebra too! I totally don't get it but ill guess.

1. it's already simplified

2. i really don't know

3. x-y+z=3 ( divide 12 by 4 to simplify)

Hope it helped, maybe it did, idk

Thx for 2 pts