Question

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Is the ordered triple (-4, 2, 3) a solution to the system of equations? Explain.
3.0 + 4y - 5z =
19
23
- 3y + z = – 11
- 2 + 2y – 2z = 1
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A. Yes, the triple satisfies all three equations.
B. No, the triple does not satisfy the first equation.
C. No

Answer 1

The ordered triple (-4, 2, 3) does not satisfy any of the given equations in the system; therefore, it is not a solution to the system.

Step-by-step explanation:

To determine if the ordered triple (-4, 2, 3) is a solution to the given system of equations, we need to substitute the values of x, y, and z into each equation and see if they satisfy all of them.

1. For the first equation 3.0 + 4y - 5z =19, substitute y = 2 and z = 3:
   3 + 4(2) - 5(3) = 3 + 8 - 15 = 11, which does not equal 19, hence this equation is not satisfied.
2. The second equation x + 23 - 3y + z = – 11, substitute x = -4, y = 2, and z = 3:
   (-4) + 23 - 3(2) + 3 = 19 - 6 + 3 = 16, which does not equal -11, hence this equation is not satisfied.
3. For the last equation -2 + 2y - 2z = 1, substitute y = 2 and z = 3:
   -2 + 2(2) - 2(3) = -2 + 4 - 6 = -4, which does not equal 1, hence this equation is not satisfied.

Since the ordered triple does not satisfy any of the given equations, it is not a solution to the system of equations.