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Solve the system of equations by elimination:

-3x - y - 3z = -8
3x + 2y + 2z = 10
-x - 3y + z = -12

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Final answer:

To solve the system of equations by elimination, we multiply and add the equations to eliminate one variable, then solve for the remaining variables.

Step-by-step explanation:

To solve the system of linear equations by elimination, we need to eliminate one of the variables by adding or subtracting the equations. Let's use the first and second equations:

Multiply the first equation by 3 and the second equation by -3 to make the coefficients of x the same:

-9x - 3y - 9z = -24x + 6y + 6z = 30

Add the two equations together:

(-9x - 3y - 9z) + (-24x + 6y + 6z) = (-24 + 30)

-33x + 3y - 3z = 6

Now let's use the first and third equations:

Multiply the first equation by 1 and the third equation by 3 to make the coefficients of x the same:

-3x - y - 3z = 3x - 9y + 3z = -36

Add the two equations together:

(-3x - y - 3z) + (3x - 9y + 3z) = (-36 - 12)

-10y = -48

Divide both sides by -10:

y = 4.8

Now substitute the value of y into any of the original equations to solve for x and z. For example, substitute y = 4.8 into the first equation:

-3x - 4.8 - 3z = -8

-3x - 3z = 3.2

This system does not have unique solutions, but the solution can be represented in terms of x and z.

User Amine KOUIS
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