Question

can someone help me with this math question?Solve the system of equations given below.

x+3z=12
-x-2y+z=10
3x+5y+2z=-7

I am really stumped. Please help! Thanks in advance!

Answer 1

You want to take your 3 equations in 3 variables to 2 equations with the same 2 variables. Since the first equation has x and z, lets see if we can eliminate the y by combining the 2nd and 3rd equations.
To eliminate y you need the coefficients to be equal and opposite. So you would want a -10 and a + 10 since you are dealing with a -2 and 5.

Multiply the second equation by 5 to get
-5x-10y + 5z = 50
Multiply the 3rd equation by 2 to bet
6x + 10y + 4z = -14

Now, combine those two equations and you will bet x + 9z =36
Now, combine this equation with the first equation. If you want to eliminate x, then multiply the first equation by negative 1.

-x -3z = -12 combine this with x+9z = 36

The x will be eliminated.
6z =48 Solve for z.

Once you have z, put it into the first equation and solve for x.

Then put your value for x and z into the second equation to find y.

Once you have (x,y,z) you should check those value in all three equations.

Answer 2

from the first: x = 12-3z
plug that into the 2nd:
-12+3z-2y+z = 10
4z - 2y = 22
2z - y = 11 , #4

plut x = 12-3z into the 3rd
36-9z +5y + 2z = -7
-7z + 5y = -43 , #5

#4 times 5 ---> 10z - 5y = 55
add this to #5
3z = 12
z = 4
in #4: 8-y = 11
y = -3
back in x = 12-3z
x = 12-12 = 0

<b>x=0 , y = -3, z = 4</b>

As you can see, there are many ways to do this.
Just wiggle the variables back and forth a bit, look for simple combinations