Question

X + y + z = 30. 2x + 3y + 4z = 100. Find the value of x, y and z ​

Answer 1

There are infinitely many solutions for x, y and z.

By elimination, we have

(2x + 3y + 4z) - 2 (x + y + z) = 100 - 2•30

⇒   y + 2z = 40

and

(2x + 3y + 4z) - 3 (x + y + z) = 100 - 3•30

⇒   -x + z = 10

If we let z = t for some real number t, then

y + 2z = 40   ⇒   y = 40 - 2t

-x + z = 10   ⇒   x = t - 10

so any solution to the system is a point belonging to the set

$\left\{ (t-10,40-2t,t) \mid t\in\mathbb R\right\}$