Question

Does the ordered triple satisfy the following system of equations?

Answer 1

Given the ordered triple:

`(-8,-5,6)`

If we are to check if it satisfies the set of equations given:

`\begin{gathered} -3y-2z=3 \\ -x+y=3 \\ 3x-3y+2z=3 \end{gathered}`

We will simply substitute the values of

`\begin{gathered} x=-8,\text{ y=-5, and z=6} \\ \text{Into the left-hand sides of the equation given and then compare with the right-hand side} \end{gathered}`

For the first equation

`\begin{gathered} -3(-5)-2(6)=15-12=3 \\ \text{The left-hand side equals the right-hand side } \end{gathered}`

For the second equation

`\begin{gathered} -(-8)+(-5)=3 \\ \text{The left-hand side equals the right-hand side } \end{gathered}`

For the third question

`\begin{gathered} 3(-8)-3(-5)+2(6)=3 \\ \text{The left-hand side equals the right-hand side } \end{gathered}`

Since the left-hand side equals the right-hand side in the three cases, the ordered triple satisfies the systems of equation.

Thus, the correct answer is Yes