# Solve the system of linear equation:(a+1)x-(b-8)y+(c-3)z=8 (a-2)x+by+(b+3)z=4 (d-1)x+(4-c)y-(d+1)+z=6

*print*Print*list*Cite

### 1 Answer

You need to eliminate a variable, hence, if you will eliminate variable y, you need to multiply the first equation by b and the second by (b-8) such that:

`b(a+1)x-b(b-8)y+b(c-3)z=8b`

`(b-8)(a-2)x+b(b-8)y+(b-8)(b+3)z=4(b-8)`

You need to add these equations such that:

`x(ab- b + ab - 8a + 16) + z(bc - 8b + b^2 - 24) = 12b - 32`

You need to eliminate variable y from the second and third equations such that:

`(a-2)(4-c)x+b(4-c)y+(b+3)(4-c)z=4(4-c)`

`-b(d-1)x-b(4-c)y+b(d+1)z=-6b`

You need to add these equations such that:

`x(4a - ac - 8 + 2c - bd + b) + z(5b - cb + 12 - 3c + bd) = 16 - 4c - 6b`

You need to eliminate one variable, either x or z, from the new two equations.

**Hence, the solution to the equations depends on the coefficients a,b,c,d.**