solve system of equation

5x+2y+z=-25
5x-3y-z=-23
3x+y+2z=-9

I would use elimination and start with the z's

Add the first plus the second to get
10x - y = -48

Double the second and add it to the third to get 13x - 5y = -55

ahhh, changed my mind, let's now switch to substitution
from above 10x - y = -48 or
y = 10x + 48

sub that into
13x - 5y = -55
13x - 5(10x + 48) = -55

etc. (I got x=5)

I am sure you can finish it from here.

I am coming up with (-5,-2,4) for my answer and I see you x=5

good job

You can tell your answers are correct by merely subbing them back into the 3 original equations, they work

TRUST YOURSELF

To solve the given system of equations, we can use the method of elimination or substitution. Let's use the substitution method to find the values of x, y, and z.

Step 1: Choose one equation to solve for a variable in terms of the other variables. Let's solve the third equation for x:

From the third equation, we get:
3x + y + 2z = -9 ---> 3x = -y - 2z - 9 ---> x = (-y - 2z - 9)/3

Step 2: Substitute the expression for the variable found in Step 1 into the other two equations. Let's substitute the expression for x into the first equation:

Substituting x = (-y - 2z - 9)/3 into the first equation, we get:
5(-y - 2z - 9)/3 + 2y + z = -25

Simplifying this equation, we have:
-5y - 10z - 45 + 6y + 3z = -75
y - 7z = -30 ---> Equation 4

Step 3: Substitute the expression for x found in Step 1 into the second equation:

Substituting x = (-y - 2z - 9)/3 into the second equation, we get:
5(-y - 2z - 9)/3 - 3y - z = -23

Simplifying this equation, we have:
-5y - 10z - 45 - 9y - 3z = -69
-14y - 13z = 24 ---> Equation 5

Now, we have two equations with two variables: Equation 4 (y - 7z = -30) and Equation 5 (-14y - 13z = 24). We can solve this system of equations using any method like elimination or substitution. Let's use substitution again.

Step 4: Solve Equation 4 for y in terms of z:

From Equation 4, we get:
y = -30 + 7z

Step 5: Substitute the expression for y found in Step 4 into Equation 5:

Substituting y = -30 + 7z into Equation 5, we have:
-14(-30 + 7z) - 13z = 24

Simplifying this equation, we get:
420 - 98z - 13z = 24
420 - 111z = 24
-111z = 24 - 420
-111z = -396
z = -396 / -111
z = 4

Step 6: Substitute the value of z found in Step 5 into Equation 4 to find y:

Substituting z = 4 into Equation 4, we have:
y - 7(4) = -30
y - 28 = -30
y = -30 + 28
y = -2

Step 7: Substitute the values of y and z found in Steps 6 and 5 into Equation 3 to find x:

Substituting y = -2 and z = 4 into Equation 3, we have:
3x + (-2) + 2(4) = -9
3x - 2 + 8 = -9
3x + 6 = -9
3x = -9 - 6
3x = -15
x = -15 / 3
x = -5

So, the solution to the system of equations is:
x = -5, y = -2, and z = 4.