Question

How do you solve this system of equations: `6x + y = 7, y + z = 2 , and 4x - z = 4`?

Answer 1

`color(maroon)(x = 1/2, y = 4, z = -2`

Explanation:

`6x + y = 7 " Eqn (1)"`

`y + z = 2 " Eqn (2)"`

`4x - z = 4 " Eqn (3)"`

`z = 4x - 4 " from Eqn (3)"`

Substituting the value of z in terms of x in Eqn (2),

`y + 4x - 4 = 2 " or " 4x + y = 6 " Eqn (4)"`

Subtracting Eqn (4) from (1),

`6x + y - 4x - y = 7 - 6`

`2x = 1 ' or x = (1/2)`

Substituting value of x in Eqn (3),

`4 * 1/2 - 4 = z " or " z = -2`

Substituting value of z in Eqn (2),

`y + (-2) = 2 " or " y = 4`

Answer 2

`x=1/2`, `y=4` and `z=-2`

Explanation:

`6x+y-(4x-z)-(y+z)=7-4-2`

`2x=1`, so `x=1/2`

Hence,

`6-1/2+y=7` or `3+y=7`, so `y=4`

Thus,

`4+z=2`, so `z=-2`