Question

justify that x=8,y=2, and z=-5 is a solution to the system below

Answer 1

To justify that x = 8, y = 2, and z = -5 is the solution to the system,

2x + y + 3z = 3

-3x + 3y - 2z = -8

5x - y + 5z = 13

Let's substitute the roots to the equation if it will be equivalent to the constant value. We get,

$\text{ 2x + y + 3z = 3}$$2(8)\text{ + (2) + 3(-5) = 3}$$16\text{ + 2 - 15 = 3}$$\text{ 3 = 3}$

Thus, x = 8, y = 2, and z = -5 is a solution to 2x + y + 3z = 3

$-3x\text{ + 3y -2z = -8}$$-3(8)\text{ + 3(2) - 29-5) = -8}$