Solve the system of equations by substitution. -3x - y - 3z = -11 z = 5 x - y + 3z = 19 (____,____,____)

Substitute z = 5: Substitute z = 5 into the first equation -3x - y - 3z = -11. -3x - y - 3*5 = -11 -3x - y - 15 = -11 -3x - y = 4Substitute z = 5: Substitute z = 5 into the second equation x - y + 3z = 19. x - y + 3*5 = 19 x - y + 15 = 19 x - y = 4Set equations equal: Notice that both equations -3x - y = 4 and x - y = 4 have the same y-term. We can use this to solve for x by setting the equations equal to each other. -3x - y = x - y -3x = x -4x = 0 x = 0Solve for x: Substitute x = 0 into one of the equations to solve for y. We'll use x - y = 4. 0 - y = 4 -y = 4 y = -4Find y and z: We have already been given z = 5, and we have found x = 0 and y = -4. The solution is the ordered triple (x, y, z). The solution is (0, -4, 5).

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Solve the system of equations by substitution. $\newline$ $-3x - y - 3z = -11$ $\newline$ $z = 5$ $\newline$ $x - y + 3z = 19$ $\newline$ (.,)

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Algebra 2

Solve a system of equations in three variables using substitution

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Q. Solve the system of equations by substitution.

\newline

-3x - y - 3z = -11

\newline

z = 5

\newline

x - y + 3z = 19

\newline

(____.____,____)

Substitute $z = 5$ : Substitute $z = 5$ into the first equation $-3x - y - 3z = -11$ .
$-3x - y - 3\times5 = -11$
$-3x - y - 15 = -11$
$-3x - y = 4$
Substitute $z = 5$ : Substitute $z = 5$ into the second equation $x - y + 3z = 19$ .
$x - y + 3\times5 = 19$
$x - y + 15 = 19$
$x - y = 4$
Set equations equal: Notice that both equations $-3x - y = 4$ and $x - y = 4$ have the same $y$ -term. We can use this to solve for $x$ by setting the equations equal to each other. $\newline$ $-3x - y = x - y$ $\newline$ $-3x = x$ $\newline$ $-4x = 0$ $\newline$ $x = 0$
Solve for x: Substitute $x = 0$ into one of the equations to solve for $y$ . We'll use $x - y = 4$ . $\newline$ $0 - y = 4$ $\newline$ $-y = 4$ $\newline$ $y = -4$
Find $y$ and $z$ : We have already been given $z = 5$ , and we have found $x = 0$ and $y = -4$ . The solution is the ordered triple $(x, y, z)$ . $\newline$ The solution is $(0, -4, 5)$ .