System of Linear Equations

Algebra Level 2

$\large 3y =\dfrac{27-9x}{3}$ $\large 9y =30-6z$ $\large x-2y-3z =6$

Given that $x,y$ and $z$ satisfy the system of equations above, find $x+y+z$ .

1 solution

A Former Brilliant Member
Jul 4, 2017

From $\color{#D61F06}(1)$ ,

$9y=27-9x$ $\implies$ $y=3-x$ $\color{#D61F06}(4)$

From $\color{#D61F06}(2)$ ,

$9y=30-6z$ $\implies$ $3y=10-2z$ $\color{#D61F06}(5)$

Subtracting $\color{#D61F06}(4)$ from $\color{#D61F06}(3)$ , we get

$y=-1-z$ $\color{#D61F06}(6)$

Substituting $\color{#D61F06}(6)$ in $\color{#D61F06}(5)$ , we get

$z=-13$

It follows that

$y=12$ and $x=-9$ .

Finally,

$x+y+z=-9+12-13=$ $\boxed{ -10}$

Nice solution bro.

genis dude - 3 years, 11 months ago