Question

I need help with solving this system by using elimination Plz help I have no idea how to do this. And plz don't just give me answers

Answer 1

First pick a variable to eliminate. Try eliminating z first from equations 1 and 2:
Multiply the second equation by -3 and add it to the first and that will get rid of the z.
Eliminate z from equations 2 and 3.
Multiply the second equation by -3 and add it to the third and that will get rid of the z.

You will be left with 2 equations and two unknowns x and y which you can solve by eliminating one of the variables, say, y.

Answer 2

I do not really understand.

Answer 3

-2x + 2y + 3z = 0 ----- equation 1
-2x - y + z = -3 ----- equation 2
2x + 3y + 3z = 5 ----- equation 3
Eliminate z from equations 1 and 2:
Multiply equation 2 by -3:
+6x + 3y - 3z = +9 ----- equation 4 Add this to equation 1:
-2x + 2y + 3z = 0 ----- equation 1
Add:
4x + 5y = 9 ----- equation 5

Now can you try the same method and eliminate z from equations 2 and 3?

Answer 4

for equation 2 and 3 is it
6x+3y-3z=9
-6x-9y-9z=-15
----------------
-6y-12z=-6 ???

Answer 5

You multiplied the wrong equation by -3. We wanted to eliminate z from equations 2 and 3. To do that, multiply the second equation by -3 and add it to to the third.

Answer 6

If you look at the coefficient of z in equation 2 it is: +1
If you look at the coefficient of z in equation 3 it is: +3
So if I multiply the second equation by -3 I will make the z coefficient -3 which when added to equation 3 will cancel out z.

Answer 7

6x+3y-3z=9
2x+3y+3z=5
-------------
8x+6y=14 ???

Answer 8

Yes.

Answer 9

Call 8x+6y=14 equation 6.

Eliminate x from equations 5 and 6.

Answer 10

4x + 5y = 9 ----- equation 5
8x + 6y =14 ----- equation 6.

Try to eliminate x. The coefficient of x in equation 5 is: 4
The coefficient of x in equation 6 is: 8
What should we do to make the coefficient of x in equation 5 to be -8 so it will cancel out with the coefficient of x in equation 6 which is +8 ?

Answer 11

times by -2??

Answer 12

Exactly! Multiply equation 5 by -2 and add it to equation 6 and the x will be gone.
You will be just left with y which you can solve easily.

Answer 13

-4y=-4

Answer 14

solve for y by dividing both sides by -4

Answer 15

=1

Answer 16

yes. Put y = 1 in equation 5 and solve for x.

Answer 17

would x be 1?

Answer 18

Yes. Put x = 1 and y = 1 in equation 2 and solve for z.
(BTW, you can put x and y values in any of the first three equations to solve for z put choose the one that is the easiest.)

Answer 19

is it 0 because...-2(1)-1+0=-3

Answer 20

Yes! Well done!

x = 1, y = 1 and z = 0 is the solution.

Answer 21

Alright thank you so much for your time!! :)

Answer 22

you are welcome.