Question

10x+ 6y + z = 7
5x - 9y - 2z = 3
15x -12y + 2z = -5
Solve x, y, z by elimination.

Answer 1

So you woukd solve using 2 equations and then you would use the answer to to solve the third equation

Answer 2

So you would multiply the second equation by 2 so that the first terms of both equations will equal the same. so here it would be 10x.
2(5x-9y-2z=3) =10x-18y-4z=6 and then you would do elimination
Subtract the two equations so you would eliminate one variable
10x-10x=0 6y-(-18y)=24y z-(-4z)=5z 7-6=1
So the new equation would be 24y+5z=1
then you would adsubtract the next two equations to eliminate the x also so you must multipy the equation by 3 for the first variables to equal:
3(5x-9y-2z=3)=15x-27y-6z=9

Answer 3

Now you must eliminate the last two equations:
15x-15x=0x -27y-(-12y)=-15y -6z-2z=-8z 9-(-5)=14
So we are left with these two equations:
-15y-8z=14 and 24y+5z=1
So I guess its easier to eliminate the z. So we must multiply both quation to get the same variable; 5(-15y-8z=14)= -75y-40z=70 and 8(24y+5z=1)=192y+40z=8

Answer 4

Now we will do elimination:
192y+75y)=267y 40z+(-40z)=0z 8+70=78
267y=78 y=78/267 y=26/89
I must have done wrong calculations becuase I am getting bad numbers

Answer 5

I used my graphic calculator and y is supposed to be 2/3 :/

Answer 6

Basically you eliminate a variable in the first two equations. Then you eliminate the same variable in the second two equations. With these two new equations you eliminate a 2nd variable and then you solve fory and then.. I am doing it in my head now so I may have made a mistake I will do it by hand and I will get back to you in a few minutes

Answer 7

Oka, thank you so much!

Answer 8

I got the answer. I will begin from the beginning

Answer 9

Oka, thank you so much!

Answer 10

alright then

Answer 11

So we will eliminate the z in all 3 equation.
You must multiply the first equation by 2: 2(10x+6y+z=7)= 20x+12y+2z=14
You must add the first two equations to eliminate z:
20x+5x=25x 12y+(-9y)=3y 2z+(-2z)=0z 14+3=17 -->25x+3y=17
Now Eliminate the last two equations:
5x+15x=20x -9y+(-12y)=-21y -2z+2z=0z 3+(-5)=-2 --> 20x-21y=-2
Now you eliminate the y in the two new equations:
First you must multiply one equation by 7 for the ys to be eliminated:
7(25x+3y=17)= 175x+21y=119
175x+20x=195x 21y+(-21y)=0y 119+(-2)=117 ---> 195x=117
117/195=x x=3/5

Answer 12

Now you must plug in the x-value into one of the 2 previous equation to find out what y equals:
25(3/5)+3y=17 3y=17-15 3y=2 y=2/3
Then you plug in the x and y value into one of the three original equations:
10(3/5)+6(2/3)+z=7 6+4+z=7 z=-3
So x=3/5 y=2/3 and z=-3
It took way longer than I had expected it to take but here is the answer.
I am a terribly slow typer when it comes to math equations

Answer 13

Oka, thank you so much!

Answer 14

Thank you so much!

Answer 15

Oka, thank you so much!

Answer 16

this really helped