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}`