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lakenyagillard79

lakenyagillard79

16.11.2020 •

Mathematics

What is the solution of the system? Use elimination. 2x + 2y +z = 7
-X – y +z = -5
x + 3y – 4z = 12

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Ответ:

amaya2387

09.02.2022

The solutions to the system of the equations by the elimination method will be:

$x=2,\:z=-1,\:y=2$

Step-by-step explanation:

Given the system of the equations

$2x\:+\:2y\:+z\:=\:7$

$-x-\:y\:+z\:=\:-5$

x+3y-4z=12

solving the system of the equations by the elimination method

$\begin{bmatrix}2x+2y+z=7\\ -x-y+z=-5\\ x+3y-4z=12\end{bmatrix}$

$\mathrm{Multiply\:}-x-y+z=-5\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y+2z=-10$

$\begin{bmatrix}2x+2y+z=7\\ -2x-2y+2z=-10\\ x+3y-4z=12\end{bmatrix}$

-2x-2y+2z=-10

$\underline{2x+2y+z=7}$

3z=-3

$\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ x+3y-4z=12\end{bmatrix}$

2x+6y-8z=24

$\underline{2x+2y+z=7}$

4y-9z=17

$\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ 4y-9z=17\end{bmatrix}$

Rearranging the equations

$\begin{bmatrix}2x+2y+z=7\\ 4y-9z=17\\ 3z=-3\end{bmatrix}$

solve 3z=-3 for z:

z=-1

$\mathrm{For\:}4y-9z=17\mathrm{\:plug\:in\:}z=-1$

solve $4y-9\left(-1\right)=17$ for y:

$4y-9\left(-1\right)=17$

4y+9=17

4y=8

y=2

$\mathrm{For\:}2x+2y+z=7\mathrm{\:plug\:in\:}z=-1,\:y=2$

solve $2x+2\cdot \:2-1=7$ for x:

$2x+2\cdot \:2-1=7$

2x+3=7

2x=4

x=2

Therefore, the solutions to the system of the equations by the elimination method will be:

$x=2,\:z=-1,\:y=2$

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Ответ:

jannaleigh

02.08.2021

Your answer should be 100%.

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