Question

Solve the system:]
3x+4y-z=0
x-2y+z=-8
4x+3y-2z=-4

Answer 1

Make z the subject of the first equation
z=3x+4y [a]
Substitute it in the second
x-2y+(3x+4y)=-8
x-2y+3x+4y=-8
4x+2y=-8
4x=-8-2y
x=-2-1/2y
Substitute x in [a]
z=3(-2-1/2y)+4y
z=-6-3/2y+4y
z=2.5y-6
So now we have x and z written in terms of y.
Substitute z and x in the third
4x+3y-2z=-4
4(-2-0.5y)+3y-2(2.5y-6)=-4
-8-2y+3y-5y+12=-4
-4y+4=-4
-4y=-8
y=2
Solve for x and z:
x=-2-1/2y
x=-2-1=-3
z=2.5y-6
z=2.5(2)-6=-1

Whoa, that was long. I do hope I didn't make a miscalculation. Do check the answers by plugging them into the original equations. Hope it helps.

Answer 2

???
Thanks so much... I will

Answer 3

you're welcome. i hope the ??? mean u understand :)

Answer 4

yes dont worry the questions mark were there b4 you answer... thanks so much

Answer 5

no prob. best of luck =)

Answer 6

I do have a nother question can I ask you?

Answer 7

sure

Answer 8

i hope it's not on systems....can't do that calc again :)

Answer 9

no lol

Answer 10

cool.

Answer 11

The sum of three numbers is 108 . The first number is 8 less than the second . The third number is 2 times the first. What are the numbers?

Answer 12

I'll guide you through this, so you'll do most of the thinking. So, lets let the first number be, say, x. okay?

Answer 13

ok

Answer 14

nice. first: x
"The first number is 8 less than the second"
so the second can be written as...?

Answer 15

x-8

Answer 16

no Y-8

Answer 17

not quite, but you have the idea. . the first number is 8 less than the second. meaning the second is greater than the first by 8

Answer 18

thus the second is...?

Answer 19

The sum of three numbers is 108 . The first number is 8 less than the second . The third number is 2 times the first. What are the numbers?
I'm sure you figured out this one eventually.
Let the first number be x.
The second will be (x+8) "The first number is 8 less than the second"
The third will be 2x. "The third number is 2 times the first"
Now, the sum of the three is 108. So we have a nice equation.
x+(x+8)+2x=108
Solve for x, then you can calculate the value of the second and third numbers. Best wishes.