Verified answer

-2z = -6

2x + 3y - z = -2

x + 2y + 3z = 9

z = 3

2x + 3y = 1

2x + 4y = 0

y = -1

x = 2

This question is actually rather nice since your instructor has basically already given you one of the variables. Let's first look at -2z = -6

In order to solve this we simply need to divide both sides of this by -2 to give you

z = 3

Now let's focus on doing some elimination with the two equations:

Equation 1: 2x + 3y - z = -2

Equation 2: x + 2y + 3z = 9

Notice that we can easily use the elimination method on the 2x and x by simply multiplying Equation 2 by -2.

-2(x + 2y + 3z = 9)

-2x -4y - 6z = -18

Now let's add Equation 1 and Equation 2 together

2x + 3y - z = -2

-2x -4y -6z = -18

______________

-y -7z = -20

(This happened because the 2x and -2x canceled each other out.)

Now we learned at the start that z = 3, right? Now we simply plug it into the equation with two variables.

-y -7(3)= -20

-y -21 = -20

Now we simply add 21 to both sides

-y = 1

Then divide by a negative 1 to get our y positive and:

y= -1

Now that we believe y = -1 and z = 3, we now simply need to plug them back into Equation 1 or Equation 2. I'll do equation 1.

2x + 3(-1) -3 = -2

2x -6 = -2

Now we'll simply add 6 to both sides to get

2x= 4

Then divide by 2 to get

x = 2

So, to satisfy all three equations, I believe x = 2, y= -1, z = 3. Make sure to check these numbers and see that they work with ALL THREE equations. Everyone makes mistakes including myself, so always check the numbers yourself.

-2z=-6 ......(1)

2x + 3y - z = -2........(2)

x + 2y + 3z = 9.........(3)

from equation (1)

-2z=-6

=> z = -6/(-2) = 3

put z = 3 into equation (2) and (3) to get equation (4) and (5)

2x + 3y - 3 = -2 ....... (4)

x + 2y + 3(3) = 9......(5)

simplify equa (4) and (5) to get equa (6) and (7)

2x + 3y = 1.......(6)

x + 2y = 0 .......(7)

from equa (7) make x the subject of the formula to get equa (8)

x = -2y.... (8)

put (8) into (6) to get

-2(2y) + 3y = 1

==> -4y + 3y = 1

==> y = -1

put y into equa (8) to get x

==> x = -2(-1)

==> x = 2

your final answer should be x = 2, y = -1, and z = 3

hope this help

now your turn ma 10 point haha

-2z = -6 or z= 3

so 2x+ 3y - z= -2 or 2x + 3y- 3 = -2 or 2x+ 3y = 1----------------------(I)

and x+ 2y + 3z = 9 or x+ 2y+ 9 = 9 or x+ 2y = 0 -------------(II)

from (I) & (II)

- y= 1 or y = -1

so x= 2

z= 3