Question

Help me solve for z y and z!! Please show work and my teacher said something about making it into a matrix?
x-3y+2z=11
-x+4y+3z=5
2x-2y-4z=2

Answer 1

I wanted to solve it by substitution or elimination, thats how we learned it in class. And im in Algebra II

Answer 2

thank you kind sir.

Answer 3

Since you have 3 equations and 3 variables, the system is also solvable by substitution. I never learned matrices though, it might be faster. ;)

Answer 4

Ty, but how would you use substitution to find each? I know how to do it for 2 variables, but not 3. My teacher doesn't explain things very well in school.

Answer 5

It's kind of the same process. You first solve for one variable in the first equation and substitute it into the 2nd and 3rd to make them have 2 variables. Then you solve for another variable in the new 2nd equation and substitute that into the 3rd, to get a solvable equation with one variable. Next you just solve for that 3rd variable and use it to find your first two.

Answer 6

I'm not really following, can you use this question ad an example and show your work?

Answer 7

add first two equations
you will have equation in two variables y and z .
y+5z=16

multiply the second equation (-x+4y+3z=5) with 2 and add to the third equation
6y+2z=12

solve these two equations for y and z
y+5z=16
6y+2z=12

can you solve these ??

Answer 8

ok i got to y+5z=16. lemme keep going...

Answer 9

wait why multiply by 2

Answer 10

x - 3y + 2z = 11
-x + 4y + 3z = 5
2x - 2y - 4z = 2

Well first you can solve for x in your first equation.
x - 3y + 2z = 11
x = 11 + 3y - 2z

Next you can substitute that x into your second equation.
-x + 4y + 3z = 5
-(11 + 3y - 2z) + 4y + 3z = 5
y + 5z = 16

Solve for y.
y + 5z = 16
y = 16 - 5z

Substitute for x & y in your third equation and solve for z.
2x - 2y - 4z = 2
2(11 + 3y - 2z) - 2(16 - 5z) - 4z = 2

Then just use your z value to find x & y.

Answer 11

Or you can also skip some of that substitution using Sami's clever manipulations :)

Answer 12

I'll be right back. I need cake. But im prepared for an all-nighter

Answer 13

i would say make your life easir with following.
add first two equations
you will have equation in two variables y and z .
y+5z=16

multiply the second equation (-x+4y+3z=5) with 2 and add to the third equation
6y+2z=12

solve these two equations for y and z
y+5z=16 ............ 1
6y+2z=12 ............. 2

from equation 1 above
y=16-5z
put in equation 2
6(16-5z)+2z=12
96-30z+2z=12
96-28z=12
28z=84
z=84/28=3
since y=16-5z=16-5(3)=1

z=3
y=1
put in any of the following equations to get x .

x-3y+2z=11
-x+4y+3z=5
2x-2y-4z=2

Answer 14

Thank you so mush both of you (:

Answer 15

wait now im confused again :/

Answer 16

\[\left[\begin{matrix}1 & -3 & 2 \\ -1 & 4 & 3 \\ 2 & -2 & -4\end{matrix}\right]\]

It would help if you could find the inverse matrix.

Answer 17

Are you still working on this?
x - 3y + 2z = 11
-x + 4y + 3z = 5
2x - 2y - 4z = 2

If so, what are confused about?

Answer 18

Use the following to check you answers:
{x = 8, y = 1, z = 3}