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Determine whether
(8,9,9) is a solution to the system.

{:[-2x+3y+4z=,47],[-5x+4y-4z=,-40],[11 x+2y-8z=,34]:}

Determine whether $(8,9,9)$ is a solution to the system. $\newline$ $\begin{array}{rr} -2 x+3 y+4 z= & 47 \\ -5 x+4 y-4 z= & -40 \\ 11 x+2 y-8 z= & 34 \end{array}$

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Write an equation word problem

Full solution

Q. Determine whether

(8,9,9)

is a solution to the system.

\newline

\begin{array}{rr} -2 x+3 y+4 z= & 47 \\ -5 x+4 y-4 z= & -40 \\ 11 x+2 y-8 z= & 34 \end{array}

Substitute values into first equation: Step $1$ : Substitute $x=8$ , $y=9$ , $z=9$ into the first equation $-2x + 3y + 4z = 47$ . $\newline$ Calculation: $-2(8) + 3(9) + 4(9) = -16 + 27 + 36 = 47$ .
Substitute values into second equation: Step $2$ : Substitute $x=8$ , $y=9$ , $z=9$ into the second equation $-5x + 4y - 4z = -40$ . $\newline$ Calculation: $-5(8) + 4(9) - 4(9) = -40 + 36 - 36 = -40$ .
Substitute values into third equation: Step $3$ : Substitute $x=8$ , $y=9$ , $z=9$ into the third equation $11x + 2y - 8z = 34$ . $\newline$ Calculation: $11(8) + 2(9) - 8(9) = 88 + 18 - 72 = 34$ .

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