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Solve the following system of equations for all three variables.-8x – 3y + 5z = -2X-2y – 5z = -94x + 7y + 5z = 4

Solve The Following System Of Equations For All Three Variables8x 3y 5z 2X2y 5z 94x 7y 5z 4 class=

Sagot :

In order to solve this system of equations, first let's add the second equation to the first and third ones:

[tex]\begin{gathered} \begin{cases}-8x-3y+5z+(x-2y-5z)=-2+(-9) \\ 4x+7y+5z+(x-2y-5z)=4+(-9)\end{cases} \\ \begin{cases}-7x-5y=-11 \\ 5x+5y=-5\end{cases} \end{gathered}[/tex]

Now, adding the two resulting equations, we have:

[tex]\begin{gathered} -7x-5y+(5x+5y)=-11+(-5) \\ -2x=-16 \\ x=8 \\ \\ 5x+5y=-5 \\ 40+5y=-5 \\ 5y=-45 \\ y=-9 \\ \\ x-2y-5z=-9 \\ 8+18-5z=-9 \\ -5z=-35 \\ z=7 \end{gathered}[/tex]

So the solution for this system is x = 8, y = -9 and z = 7.

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