Solve the system: x-3y=-10 // 3x+2y-2z=-7 // -x+3y+z=15. The solution is x= ?, y=?, and z=?

Question

The question is lined up like this:

x-3y=-10

3x+2y-2z=-7

-x+3y+z=15

Answer 1

The question is lined up like this:

x-3y=-10 .... (1)

3x+2y-2z=-7..... (2)

-x+3y+z=15..... (3)

Get x from (1)

x = 3y -10

Plug in these in (2) and (3)

( 2 ) becomes

9y - 30 -2z = -7

or 9y -2z = 23 .... (4)

(3 ) becomes

-3y +10 +3y +z = 15

z+10 =15

or z= 5

Plug in z= 5 in (4)

9y -10 = 23

9y = 33

y = 33/9 = 11/3

plug in y =11/3 in (1)

x- 3 (11/3 ) = -10

x= -10 +11

x = 1 , y=11/3 , z= 5

Answer 2

First, use the 1st equation to get an equation for x as a function of y. Then, use that to replace y in th other 2 equations. this gives a pair of equations in y and z. this pair can be solved using the standard methods.

Answer 3

x-3y=-10

3x+2y-2z=-7

-x+3y+z=15

add 1st and 3rd equations:

x-3y = -10

-x + 3y + z = 15

z = 5

substitute z = 5 into 2nd and 3rd equations:

3x+2y-2*5 =-7

3x + 2y = 3

-x + 3y + 5 = 15

-x + 3y = 10

multiply 3rd equation by 3

-3x + 9y = 30

add 2nd and 3rd equation

11y = 33

y = 3

substitute y = 3 into first equation:

x-3*3=-10

x = -1

so x = -1, y = 3, z = 5