Question

The following system has a solution: x=10, y=-3, z=14

Answer 1

False

Explanation:

In this problem, we have the following System of Three Equations in Three Variables, so our goal is to determine whether
`x=10, \ y=-3, \ z=14` is the solution to this system, that is, the ordered triple
`P(x,y,z)` where three planes intersect.

The easier way to find the answer is to plug in the x, y and z values in the equations and figure out whether the equations satisfy the solutions. Then:

`First \ Equation: \\ \\ 3(10)+7(-3)-14=-5 \\ \\ It \ satisfies \ the \ first \ equation \\ \\ \\ Second \ Equation: \\ \\ 9(10)-(-3)-4(14)=37 \\eq 17 \\ \\ It \ doesn't \ satisfy \ the \ second \ equation`

STOP HERE! Since the x, y an z values doesn't satisfy the second equation, the
`x=10, \ y=-3, \ z=14` is not the solution to the system of equations.