Question

Determine whether the ordered triple is a solution to the

system>
-4x-5y-z=18
-2x-5y-2z=12
-2x+5y+2x=4
a. (0,1, -2)
b. (-4,0, -2)

Answer 1

a. No

b. Yes (-4, 0, -2) is the solution

Explanation:

You want to know if the offered solution vectors are actually solutions to the system of equations ...

• -4x -5y -z = 18
• -2x -5y -2z = 12
• -2x +5y +2x = 4

Solution

A solution to the system will result in all of the equations being true. That is, when the coefficients are multiplied by the variable values, the result is that shown on the right side of the equation.

The attached matrix multiplication does that precise function. For the column vector shown in choice A, the result is different from the given constants. A is not a solution.

For the column vector shown in choice B, the result is (18, 12, 4), matching the constants on the right in the given equations. B is the solution to the system.

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