algebra help please?

Question

i have three equations
1) 5x-2y+z=11
2) 3x+4y-2z= -9
3)-2x-y+4z=8

please solve and show me how you did it. thanks alot

Answer 1

There are several ways: solve and substitute, multiply and combine, matrices,...

I'll choose the multiply & combine method:

5x - 2y + z = 11
3x + 4y - 2z = -9

Mulitply the first by 2 and add them together

10x - 4y + 2z = 22
3x + 4y - 2z = -9
--------------------------
13x = 13
x = 1

Now do it again for another variable (you can substitute 1 in for x now):

3 + 4y - 2z = -9
-2 - y + 4z = 8

Mulitply the second by 4 and combine:

3 + 4y - 2z = -9
-8 - 4y + 16z = 32
-----------------------
-5 + 14z = 23
14z = 28
z = 2

Now you can substitute for x and z in any equation and get y:

-2 - y + 8 = 8
-y = 2
y = -2

And there you have it! All three variables can be plugged into all three equations above and their correctness proven. QED

Answer 2

mult 1st by 2 and add to 2nd 13x=13, x=1
put x =1 in 2nd and 3rd 4y - 2z = -12
-y +4z = 6
top by 2 and add
7y = -18 y = +18/7
into -y +4z = 6 gives z=6/7

hope this helps. there are powerful tools to solve systems of equations.

Answer 3

x=1, z=2, y=-2

you must first eliminate the variable x using the first 2 equations, multiply the first equation with 2, and add it to the second equation, then you get the value of x=1, plug the x value in any 2 of the equations to get two equations having y,and z, then eliminate y by adding the 2 equations we get z=2 plug x=1 and z=2 in any of the equations and simplify to get the value of y=-2

Answer 4

(1)*2
10x-4y+2z=22
3x+4y-2z=-9
adding
13x=13
x=1
5x-2y+z=11
4x+2y-8z=-16
adding
9x-7z=-5
sub x=1 z=2
sub x=1 and z=2(1)
5-2y+2=11
-2y=4
y=-2
so x=1;y=-2;z=2

Answer 5

x=1
y= -2
z=2

Answer 6

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