Question

How do you solve the system of equations: `x+y+z = 105`, `10y-z = 11`, `2x-3y = 7` ?

Answer 1

`x=17`, `y=9` and `z=79`

Explanation:

Given:

`x+y+z = 105`

`10y-z = 11`

`2x-3y = 7`

Add the first two equations together to eliminate `z` and get:

`x+11y = 116`

Multiply this equation by `2` to get:

`2x+22y = 232`

Subtract the original third equation to eliminate `x` and get:

`25y = 225`

Divide both sides by `25` to get:

`color(blue)(y = 9)`

Substitute this value of `y` into the third equation to get:

`2x-27 = 7`

Add `27` to both sides to get:

`2x = 34`

Divide both sides by `2` to get:

`color(blue)(x = 17)`

Substitute the values for `x` and `y` into the first equation to get:

`17+9+z = 105`

Subtract `26` from both sides to get:

`color(blue)(z = 79)`