algebra buffs please help?

Question

i have three equations
1) x-y= -1
2) 9x+3z= 3
3) 2y+z= 2

solve and please show me how to do this. i need the help to understand it myself. thanks

Answer 1

solve the 1st and 2nd to get an equation in y and z and then use the third and solve to getall the three
9x-9y=-9
9x+3z=3
subtracting
-9y-3z=-12
6y+3z=6 (eqn. 3 *2)
adding
-3y=-6
y=2
sub in 6y+3z=6
z=-2
sub in eqn.1
x=1
the solution set is{1,2,-2}
you can do thechecing for me

Answer 2

1) x - y = -1 add y to both sides
x = y -1

3) 2y + z = 2 add -2y to both sides
z = 2 - 2y

2) 9x + 3z = 3 plug in both and solve

9 ( y - 1 ) + 3 ( 2 - 2y ) = 3
9y - 9 + 6 - 6y = 3
3y - 3 = 3
3y = 6
y = 2

So x - 2 = -1
x = 1
And 2 ( 2 ) + z = 2
4 + z = 2
z = -2

So your answer is x = 1, y = 2 and z = -2

Answer 3

1)

Solving for x

x - y = - 1

x - y + y = - 1 + y

x = - 1 + y

- - - - - -

Solving for y

x - y = - 1

x - y - x = - 1 - x

- y = - 1 - x

- 1( - y) = -1(- 1) - 1(- x)

y = 1 + x

- - - - - - - - - - - - - - - - - - - -

2).

Solve for x

9x + 3z = 3

9x + 3z - 3z = 3 - 3z

9x = 3 - 3z

9x/9 = 3/9 + 3z/9

x = 1/3 + z/3

z = z/3

- - - - - - - -

Solve for z

9x + 3z = 3

9x + 3z - 9x = 3 - 9x

3z = 3 - 9z

3z/3 = 3/3 - 9z/3

z = 1 - 3z

- - - - - - - - - - - - - - - - - -
3).

solve for y

2y + z = 2

2y + z - z = 2 - z

2 y = 2 - z

2y/2 = 2/2 - z/2

y = 1 - z/2

- - - - - - - -

Solve for z

2y + z = 2

2y + z - 2y = 2 - 2y

x = 2 - 2y

- - - - - - - -s-

Answer 4

Take the first one
x = y - 1 [A]
Take the third one
z = 2 - 2y [B]
Put these values in the second one and solve.
9(y-1) + 3(2-2y) = 3.
Solve for y, then find x and z from eq [A] and [B]

Answer 5

from equation 1
x=y-1
from equation 3
z=2-2y
substituting these in equation 2
we have
9[y-1]+3[2-2y]=3
9y-6y=3+9-6
3y=6
y=2
x=1
z=-2

Answer 6

y=2
x=1
z=-2